Answer:
$25471.7
Step-by-step explanation:
1.06*25471.7=27000.002
Hope this helps
Jerel runs 5 days each week. On each of 4 days, he runs 2.3 km. If Jerel runs a total of 14 km, how many kilometers does he run on the fifth day? a3.8km b4.8km c5.8km d4.7km
Answer:19
Step-by-step explanation:
It costs $6 per hour for a park to water the grass. How much will it cost to water the grass for
7/3
hours?
Answer:
I think the answer is $14 hope this helps!
Step-by-step explanation:
i need help ////////
Answer:
[tex]1\frac{1}{2}[/tex] miles = 7920 feet
2[tex]\frac{1}{2}[/tex] miles = 13200 feet
3[tex]\frac{1}{2}[/tex] miles = 18480 feet
4[tex]\frac{1}{2}[/tex] miles = 23760 feet
5[tex]\frac{1}{2}[/tex] miles = 29040 feet
6[tex]\frac{1}{2}[/tex] miles = 34320 feet
Explanation:
1 mile = 5280 feet
[tex]\frac{1}{2}[/tex] miles = 2640 feet
to convert miles into feet, multiply the whole numbers by 5280 and add 2640 to find your overall feet
2[tex]\frac{1}{2}[/tex] : 2 x 5280 + 2640 = 13200 ft
3[tex]\frac{1}{2}[/tex] : 3 x 5280 + 2640 = 18480 ft
4[tex]\frac{1}{2}[/tex] : 4 x 5280 + 2640 = 23760 ft
5[tex]\frac{1}{2}[/tex] : 5 x 5280 + 2640 = 29040 ft
6[tex]\frac{1}{2}[/tex] : 6 x 5280 + 2640 = 34320 ft
28.
Car A and car B are 120 km apart. If they move towards each other, they will meet in 1 hour. If they
move in the same direction, car A will catch up with car B in 5 hours. Find the speed of car A and
the speed of car B. (Assume that the speeds of the cars are constant.)
can somebody help me solve for x.
Answer:
8/3
Step-by-step explanation:
x : 4 = 4 : 6
x = 16/ 6
x = 8/3
Suppose that a committee is studying whether there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours. Construct a 95% confidence interval for the population mean time wasted. Which distribution should you use for this problem
Answer:
The t-distribution is used, as we have the standard deviation of the sample.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
Step-by-step explanation:
We have the standard deviation for the sample, which meas that the t-distribution should be used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 81 - 1 = 80
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 80 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.99
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.99\frac{4}{\sqrt{81}} = 0.88[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 8 - 0.88 = 7.12 hours.
The upper end of the interval is the sample mean added to M. So it is 8 + 0.88 = 8.88 hours.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
In a recent academic year, many public universities in the United States raised tuition and fees due to a decrease in state subsidies. The change in the cost of tuition, a shared dormitory room, and the most popular meal plan from the previous academic year for a sample of 10 public universities were as follows:
$1,589, $593, $1,223, $869, $423, $1,720, $708, $1,425, $922 and $308.
a. What is the mean and median change in the cost? (Explain how you obtain your answer.)
b. What is the five-number summary of the change in the cost? (Explain how you obtain your answer.)
c. What is the standard deviation of the change in the cost? (Explain how you obtain your answer.)
d. The middle 50% of the change in the cost is spread over what value? (Explain how you obtain your answer.)
e. What is the coefficient of variation of the change in cost? (Explain how you obtain your answer.)
f. What are the (absolute values of) the Z scores of the change in cost?
Answer:
1. mean = 980 median = $895.5
2. 308, 593, 895.5, 1425, 1720
3. 491.7978
4. 895.5
5. 50.28%
Step-by-step explanation:
1. mean $1,589+$593+$1,223+$869+$423+$1,720+$708+$1,425+$922+$308/10
= 9780/10
= $978
median
We first arrange the values in ascending order
308,423,593,708,869,922,1223,1425,1589,1720
number of observation is even so we pick the 2 values in the middle and divide by 2
= 869+922/2
= $1791/2
$895.5
2. five number summary of change
the botom half of th dta set = 308,423,593,708,869
minimum value = 308
n = 5
median = 593 = q1
from 1, q2 = median = $895.5
the upper half of data
922,1223,1425,1589,1720
n = 5
median = $1425
maximum value = $1720
the five number summary of change in cost is therefore
308, 593, 895.5, 1425, 1720
3. standard deviation
[tex]s =[\sqrt{x-barx} ]^{2} \frac{1}{n-1}[/tex]
bar x is the mean = 978
($1,589-978)²+ ($593-978)²+ ($1,223-978)²+ ($869-978)+ ($423-978)²+ $1,720-978)²+($708-978)²+ ($1,425-978)²+ ($922-978)²+ ($308-978)²
= 2176786
=[tex]\sqrt\frac{1}{10-1} {2176786} \\\sqrt{ \frac{2176786}{9}[/tex]
= [tex]\sqrt{241865.1}[/tex]
= 491.7978
4. middle 50% is spread over the median, which is 895.5
5. coefficient of variation
= s/bar x * 100
= 491.7978/978 * 100
= 49179.78/978
= 50.28%
6. z score = x - mean/s
x = 1589
= 1589-978/491.7978
= 1.2424
for x = 593
593-978/491.7978
= -0.7828
= 0.7828
for x = 1223
1223-978/491.7978
= 0.4982
for x = 869
869-978/491.7978
= -0.2216
= 0.2216
for x = 423
423-978/491.7978
= -1.1285
= 1.1285
x = 1720
1720-978/491.7978
z = 1.5088
for x = 708
708-978/491.7978
= -0.5490
= 0.5490
for x = 1425
1425-978/491.7978
= 0.9089
for x = 922
922-978/491.7978
= -0.1139
= 0.1139
for x = 308
308-978/491.7978
= -1.3624
= 1.3624
Quadrilateral GHIJ is dilated by a scale factor of 22 to form quadrilateral G'H'I'J'. What is the measure of side H'I'?
Answer:
[tex]H'I = 48[/tex]
Step-by-step explanation:
Given
See attachment for complete question.
From the attachment, we have:
[tex]GH=16.5[/tex]
[tex]HI =24[/tex]
[tex]IJ = 17[/tex]
[tex]JG =32.2[/tex]
[tex]k = 2[/tex] --- Scale factor
Required
Find H'I
The corresponding side of H'I is HI.
So:
H'I is calculated as:
[tex]H'I = k * HI[/tex]
This gives:
[tex]H'I = 2 * 24[/tex]
[tex]H'I = 48[/tex]
Answer I to j is 42
Step-by-step explanation:
A cone in the diagram below has a radius (r) of 10mm and its height (h) is 24mm calculate the length of the slant height
Answer:
26mm
Step-by-step explanation:
by the Pythagorean theorem,
[tex]x^2=10^2+24^2\\x^2=676\\x=26[/tex]
Lucy and Ayu sold a total of 1,080 iPads. Lucy sold 7 times as many as Ayu. How many did each sell
Answer:
let L=lucy and A=ayu
l+a=1080
l=7a 7a+a=1080
8a=1080 8a/8=1080/8
ayu=135
l=7a l=7×135
l=945 so:-135+945=1080
Lucy sold 945 iPads and Ayu sold 135 iPads
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
For given question,
Let Lucy and Ayu sold 'x' and 'y' iPads respectively.
Lucy and Ayu sold a total of 1,080 iPads.
So, we get an equation,
⇒ x + y = 1080 ...............(i)
Lucy sold 7 times as many as Ayu.
So we get the second equation as,
⇒ x = 7y ................(ii)
Substitute above value of x in equation (i)
⇒ x + y = 1080
⇒ 7y + y = 1080
⇒ 8y = 1080
⇒ y = 135
This means, Ayu sold 135 iPads
Substitute above value of y in equation (ii)
⇒ x = 7(135)
⇒ x = 7 × 135
⇒ x = 945
This means, Lucy sold 945 iPads.
Therefore, Lucy sold 945 iPads and Ayu sold 135 iPads
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Help rn ahhhh please
Answer:
117π or 367.56634047
Step-by-step explanation:
Volume = π × r² × h (r=radius and h=height)
Volume = π × 4² × 13
Volume = π × 9 × 13
Volume = π × 117
Volume = 117π
Q1. If sinθ = 3/5 and cosθ = 4/5, Find the value of tanθ (Use Pythagorean Identity)
Q2. If sinθ = 3/5 and cosθ = 4/5, Find the value of tanθ (Use Trignometric Identity)
Step-by-step explanation:
[tex]sinθ = \frac{3}{5} \: \: cosθ = \frac{4}{5} \\ now \\ tanθ = \frac{sinθ}{cos θ } \\ = \frac{3}{5 } \div \frac{4}{5} \\ = \frac{3}{5} \times \frac{5}{4} \\ = \frac{3}{4} [/tex]
Hope it will help :)❤
A farmer knows that a grocery store will reject a shipment of his vegetables if more than 4% of the vegetables contain blemishes. He inspects a large truckload of tomatoes to determine if the proportion with blemishes (p) exceeds 0.04. He selects an SRS of 150 tomatoes from the more than 2,000 tomatoes in the truck. Suppose that 8 tomatoes sampled are found to have blemishes. Which of the assumptions for inference about a proportion is violated, if any?
a. Large Counts: np > 10
b. Large Counts: n(1 – p) > 10
c. The sample is a random sample of the entire population.
d. 10% condition: the sample size is less than 10% of the population.
e. There do not appear to be any violations.
Answer:
Assumption A is violated
Step-by-step explanation:
x = number of blemishes = 8
n = sample size = 150
proportion = x/n = 8/150 = 0.0533
1. large counts: np> 10
= 150 * 0.0533 >10
= 7.995 > 10
this assumpton is obviously violated. 7.995 is not greater than 10
2. Large Counts: n(1 - p) > 10
150(1-0.0533)>10
150-7.995 > 10
142.005> 10
there is no violation. The assumption is satisfied
3. This assumption is satisfied. this is because the tomatoes were selected using simple random sampling.
4. 10% of the population = 0.1 * 2000 = 200
the sample size = 150
150 < 200
this assumption is satisfied
00:00
The city council in Middlefield wants to know if residents are in favor of a traffic camera at the main intersection in town. Drag tiles to match each
term to the example it best describes. Each tile may be used only once.
Representative Sample
Population
NOT a Representative Sample
Term
Example
Drivers who reside in Middlefield
Residents of Middlefield
Residents randomly chosen from the town register
Answer:
Matching Tiles with Terms:
Term Example
NOT a Representative Sample Drivers who reside in Middlefield
Population Residents of Middlefield
Representative Sample Residents randomly chosen from the
town register
Step-by-step explanation:
Population includes all the residents of Middlefield.
Representative Sample is a population subset that accurately reflects the characteristics of the population. For example, the subset of residents who are randomly chosen from the town register is an unbiased and representative sample.
NOT a Representative Sample: For example, drivers who reside in Middlefield do not represent the characteristics of the population of Middlefield.
The length of stay at a specific emergency department in Phoenix, Arizona, in 2009 had a mean of 4.6 hours with a standard deviation of 2.9. Assume that the length of stay is normally distributed.
a. What is the probability of a length of stay greater than 10 hours?
b. What length of stay is exceeded by 25% of the visits?
c. From the normally distributed model, what is the probability of a length of stay less than 0 hours? Comment on the normally distributed assumption in this example.
Answer:
a) the probability of a length of stay greater than 10 hours is 0.03144
b) the length of stay is exceeded by 25% of the visits is 6.5 hrs
c)
P( X < 0 ) = 0.0559
The probability of length of stay less than 0 hours is 0.0559, length of stay cannot be less than 0. When the normal model is used, we assume that the LOF is approximately normally distributed.
The LOF is better modeled by the normal distribution near the mean and worse in the tails.
The probabilities in the left tail for the vales of X < 0 can be neglected.
Step-by-step explanation:
Given that;
mean μ = 4.6
standard deviation σ = 2.9
let x represent length of stay;
a. What is the probability of a length of stay greater than 10 hours?
p( x > 10 ) = p( x-μ/σ > 10-4.6 / 2.9 )
= p( Z > 1.86)
= P( Z < - 1.86 )
FROM THE Z SCORE TABLE;( Z < - 1.86 ) = 0.03144
p( x > 10 ) = 0.03144
Therefore, the probability of a length of stay greater than 10 hours is 0.03144
b) What length of stay is exceeded by 25% of the visits?
p( X > x ) = 0.25
so
p( X < x ) = 0.75
p( x-μ/σ < x-4.6 / 2.9 ) = 75
p( Z < x-4.6 / 2.9 ) = 0.75 ----- 1
also, from the standard normal table; P( Z < 0.67 ) = 0.75 ------ 11
from equation 1 and 11
x-4.6 / 2.9 = 0.67
x-4.6 = 2.9 × 0.67
x - 4.6 = 1.943
x = 4.6 + 1.943
x = 6.543 ≈ 6.5
Therefore, the length of stay is exceeded by 25% of the visits is 6.5 hrs
c) From the normally distributed model, what is the probability of a length of stay less than 0 hours?
P( X < 0 ) = p( x-μ/σ < 0-4.6 / 2.9 )
= P( Z - 1.59)
from table;( Z - 1.59) = 0.0559
P( X < 0 ) = 0.0559
The probability of length of stay less than 0 hours is 0.0559, length of stay cannot be less than 0. When the normal model is used, we assume that the LOF is approximately normally distributed.
The LOF is better modeled by the normal distribution near the mean and worse in the tails.
The probabilities in the left tail for the vales of X < 0 can be neglected.
What is the value of the expression below when x=7?
6x+ 10
A. 52
B. 67
C. 42
D.77
Answer:
52
Step-by-step explanation:
when a letter is next to a number like that and they tell u what the letter is u times it so 6x7+10=52 hope this helped :P
In ΔVWX, x = 9.1 inches, w = 5.4 inches and ∠W=161°. Find all possible values of ∠X, to the nearest 10th of a degree
Answer:
NO POSSIBLE TRIANGLES
Step-by-step explanation:
Answer:
no possible triangles
Step-by-step explanation:
On Saturday, Ahmed walks his dog 0.5 mile. On the same day, Latisha walks her dog 0.7 times as far as
Ahmed walks his dog.
How far does Latisha walk her dog on Saturday?
Latisha walks her dog mile(s) on Saturday. I have it due by tomorrow at 7 am please help, don’t put the links!!
Help please!!!!!! I don't have a lot of time
Answer:
Its 5,...................
Answer:
5
Step-by-step explanation:
simplify the exponent
35/8-1
simplify
35/7
simplify
5
a new optical illusion is posred on the internet. Write a recursive formula to describe the pattern. The, write the explicit formula that can be used to find the number of times the optical illusionis shared after eight hours.
Answer:
hope this helps
The solution is 3,27,680
The geometric progression is given by aₙ = a ( r )ⁿ⁻¹ , where r = 4 is the common ratio and after 8 hours a₈ = 3,27,680
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the first term of the geometric sequence be a₁ = 20
Let the second term a₂ = 80
So , the common ratio r = second term / first term
On simplifying the equation , we get
Common ratio r = 80/20
Common ratio r = 4
Now , the explicit formula for the GP is
aₙ = a ( r )ⁿ⁻¹ , where n is the number of hours
aₙ = 20 ( 4 )ⁿ⁻¹
So , after 8 hours ,
Substitute the value of n = 8 in the equation , we get
a₈ = 20 ( 4 )ⁿ⁻¹
a₈ = 20 ( 4 )⁷
a₈ = 3,27,680
Therefore , the value of a₈ = 3,27,680
Hence , the equation is aₙ = 20 ( 4 )ⁿ⁻¹
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HELP PLEASE BRAINLYIST
Examine the diagram. It is not drawn to scale.
Wh at is the m angle 3?
Х
m angle 3=
Answer:
isn't it just 50°
Step-by-step explanation:
180=a straight line.
you are given 75° and 55°
75+55=130
180-130
Answer:
105
Step-by-step explanation:
Chupapi
Some loser deleted my answers
That's why it says 1 answer and 1.5k people helped
The distance around the outside of an apartment is 0.3 mile. Keira ran 0.1 of the distance during her lunch. How far did she run?
Answer:
0.1
Step-by-step explanation:
the measures of the angles of a triangle are shown in the figure below. solve for x
Answer:
Brainliest????
Step-by-step explanation:
X=23°
Can y’all help me on question 27?!
Answer:
B and D
Step-by-step explanation:
A would be:
57 + 2j
C would be:
13-t
The diameter of a circle is 3 meters. What is the circumference?
Answer:
C≈9.42m
Using any of this formulas
C=2πr
C=2πrd=2r
Solution:
C=πd=π·3≈9.42478m
Which would be a good estimate for the tax on $97.95 if the tax is 9.5%?
$12
$10.50
$10
$8.50
a normal distribution has a mean of 56 and a standard deviation of 8. Find the percentage of data values that are in the given interval. Use the curve to aid you.
Answer:
12) Between 40 and 64 = 0.815
13) Between 32 and 40 = 0.0235
14) Between 56 and 64 = 0.34
15) At most 56 = 0.515
16) At least 72 = 0.025
17) At most 64 = 0.855
Explanation:
To answer this, we will convert each of the values into their standardized form to make this easier.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ
x = Each value
μ = Mean = 56
σ = Standard deviation = 8
12) Between 40 and 64
For 40,
z = (x - μ)/σ = (40 - 56)/8 = (-16/8) = -2
For 64
z = (x - μ)/σ = (64 - 56)/8 = (8/8) = 1
So,
Between 40 and 64 = Between -2 and 1
From the curve, noting that the central point is the mean, with standard score of 0, the lines before it move in step of 1 standard deviation towards the negative side, that is, -1, -2, etc. And the lines before the central point move towards the positive side, that is, 1, 2, 3, etc.
So,
Between -2 and 1 = 0.135 + 0.34 + 0.34 = 0.815
13) Between 32 and 40
For 32,
z = (x - μ)/σ = (32 - 56)/8 = (-24/8) = -3
For 40,
z = (x - μ)/σ = (40 - 56)/8 = (-16/8) = -2
So,
Between 32 and 40 = Between -3 and -2 = 0.0235
14) Between 56 and 64
For 56,
z = (x - μ)/σ = (56 - 56)/8 = (0/8) = 0
For 64,
z = (x - μ)/σ = (64 - 56)/8 = (8/8) = 1
Between 56 and 64 = Between 0 and 1 = 0.34
15) At most 56
For 56,
z = (x - μ)/σ = (56 - 56)/8 = (0/8) = 0
At most 56 = At most 0 = 0.0015 + 0.0235 + 0.15 + 0.34 = 0.515
All the regions before z = 0)
16) At least 72
For 72,
z = (x - μ)/σ = (72 - 56)/8 = (16/8) = 2
At least 72 = At least 2 = 0.0235 + 0.0015 = 0.025
(All the regions from z = 2 to the end)
17) At most 64
For 64,
z = (x - μ)/σ = (64 - 56)/8 = (8/8) = 1
At most 64 = At most 1 = 0.0015 + 0.0235 + 0.15 + 0.34 + 0.34 = 0.855
(All the regions before z = 1)
Hope this Helps!!!
Find the slope of the line
O 1/3
O 6/2
0 -3/1
03/1
Answer:
6/2
Step-by-step explanation:
The slope of the given line is 3/1, Option D is correct.
The given line is passing through the points (1, 3) and (-1, -3)
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Plug in the values of points (1, 3) and (-1, -3) in the formula.
m= -3-3/-1-1
=-6/-2
Divide numerator and denominator by 2
We get 3
Slope of the line is 3.
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g The average midterm score of students in a certain course is 70 points. From the past experience it is known that the midterm scores in this course are Normally distributed. If 29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points, find the probability that the average midterm score of these students is at most 75 points. (Round your final answer to 3 places after the decimal point).
Answer:
0.98 = 98% probability that the average midterm score of these students is at most 75 points.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average midterm score of students in a certain course is 70 points.
This means that [tex]\mu = 70[/tex]
29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points.
This means that [tex]\sigma = 13.15, n = 29, s = \frac{13.15}{\sqrt{29}} = 2.44[/tex]
Find the probability that the average midterm score of these students is at most 75 points.
This is the pvalue of Z when X = 75. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{75 - 70}{2.44}[/tex]
[tex]Z = 2.05[/tex]
[tex]Z = 2.05[/tex] has a pvalue of 0.98.
0.98 = 98% probability that the average midterm score of these students is at most 75 points.
Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct, Since Richard has not attended a class recently, he doesn't know any of the answers, Assuming that Richard guesses on all 10 questions. Find the indicated probabilities.
A) What is the probability that he will answer all questions correctly?
B) What is the probability that he will answer all questions incorrectly?
C) What is the probability that he will answer at least one of the questions correctly?
Then use the fact that P(r1) = 1 P(r = 0).
D) What is the probability that Richard will answer at least half the questions correctly?
Answer:
a) 0.0000001024 probability that he will answer all questions correctly.
b) 0.1074 = 10.74% probability that he will answer all questions incorrectly
c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.
d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Each question has five answers, of which only one is correct
This means that the probability of correctly answering a question guessing is [tex]p = \frac{1}{5} = 0.2[/tex]
10 questions.
This means that [tex]n = 10[/tex]
A) What is the probability that he will answer all questions correctly?
This is [tex]P(X = 10)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024[/tex]
0.0000001024 probability that he will answer all questions correctly.
B) What is the probability that he will answer all questions incorrectly?
None correctly, so [tex]P(X = 0)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]
0.1074 = 10.74% probability that he will answer all questions incorrectly
C) What is the probability that he will answer at least one of the questions correctly?
This is
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
Since [tex]P(X = 0) = 0.1074[/tex], from item b.
[tex]P(X \geq 1) = 1 - 0.1074 = 0.8926[/tex]
0.8926 = 89.26% probability that he will answer at least one of the questions correctly.
D) What is the probability that Richard will answer at least half the questions correctly?
This is
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264[/tex]
[tex]P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055[/tex]
[tex]P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008[/tex]
[tex]P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001[/tex]
[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0[/tex]
So
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328[/tex]
0.0328 = 3.28% probability that Richard will answer at least half the questions correctly