Answer:
a) 0.0016 = 0.16% probability that the sample mean is at least $30.00.
b) 0.8794 = 87.94% probability that the sample mean is greater than $26.50 but less than $30.00
c) 90% of sample means will occur between $26.1 and $28.9.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, 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.
In this question, we have that:
[tex]\mu = 27.50, \sigma = 7, n = 68, s = \frac{7}{\sqrt{68}} = 0.85[/tex]
a. What is the likelihood the sample mean is at least $30.00?
This is 1 subtracted by the pvalue of Z when X = 30. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem, we have that:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{30 - 27.5}{0.85}[/tex]
[tex]Z = 2.94[/tex]
[tex]Z = 2.94[/tex] has a pvalue of 0.9984
1 - 0.9984 = 0.0016
0.0016 = 0.16% probability that the sample mean is at least $30.00.
b. What is the likelihood the sample mean is greater than $26.50 but less than $30.00?
This is the pvalue of Z when X = 30 subtracted by the pvalue of Z when X = 26.50. So
From a, when X = 30, Z has a pvalue of 0.9984
When X = 26.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{26.5 - 27.5}{0.85}[/tex]
[tex]Z = -1.18[/tex]
[tex]Z = -1.18[/tex] has a pvalue of 0.1190
0.9984 - 0.1190 = 0.8794
0.8794 = 87.94% probability that the sample mean is greater than $26.50 but less than $30.00.
c. Within what limits will 90 percent of the sample means occur?
Between the 50 - (90/2) = 5th percentile and the 50 + (90/2) = 95th percentile, that is, Z between -1.645 and Z = 1.645
Lower bound:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.645 = \frac{X - 27.5}{0.85}[/tex]
[tex]X - 27.5 = -1.645*0.85[/tex]
[tex]X = 26.1[/tex]
Upper Bound:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.645 = \frac{X - 27.5}{0.85}[/tex]
[tex]X - 27.5 = 1.645*0.85[/tex]
[tex]X = 28.9[/tex]
90% of sample means will occur between $26.1 and $28.9.
In which step did the veterinarian make the first error?
Step 1
Step 2
Step 3
Step 4
Answer:step 3 Step-by-step explanation: because it is right and i took the test edge 2021
Triangle TSR is similar to Triangle TNM
Which statement below is true?
Answer:
[tex]\overline{SR}\sim \overline{NM}[/tex]
Step-by-step explanation:
In similar triangles, all corresponding sides are similar. Since [tex]SR[/tex] corresponds with [tex]NM[/tex], they are similar. None of the other answer choices use corresponding sides.
y = |cosx|
any body can answer my question
What is the solution to this equation? 3 square root (1/8-x)=-1/2
NEED ANSWER ASAP please
Answer:
x is 10
Step-by-step explanation:
Which ordered pair is in the solution set of the system of inequalities shown in the graph below
The ordered pair is in the solution set of the system of inequalities shown in the graph will be (-2, -1)
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
The shaded portion will be conider as the dashed line joining points (-2, -2) and (3, 3).
Anf for the equation x - 1 > 0, x > 1
The shaded portion to the right of the dashed line joining points (1, 5) and (1, -3).
The portion affected by the two shadings would be the portion common to the right of the dashed line joining points (1, 5) and (1, -3) and under the dashed line joining points (-2, -2) and (3, 3).
The ordered pair is in the solution set of the system of inequalities shown in the graph will be (-2, -1)
Learn more about inequalities here:
https://brainly.com/question/27425770
#SPJ5
What is the volume of the rectangular prism?
Answers:
2/9 FT 3
10 FT 3
1 1/9 ft 3
3 1/3 FT 3
Answer:
3 1/3 FT 3
Step-by-step explanation:
im not sure if this right but i tried lol
Answer:
There is not enough info you need to add a picture of the box to measure it.
how many pounds does a 77kg man weigh? (hint: there are 2.2pounds in 1 kg)
Will mark brainliest!!!solve for each variable
Which of the following fractions is equivalent to -88/248 in least common terms?
Answer:
Its would be A -11/31
Step-by-step explanation:
The ability to influence another is a function of ______
= Dependency
Step-by-step explanation:
The ability to influence another is a function of dependency hahahaja
The sum of two numbers is 52. The difference of the two numbers is 6. Find the two numbers.
b) Write the equations.
Answer:46
Step-by-step explanation:
Find the value of x. Then classify the triangle by its angles.
Answer:
x
Step-by-step explanation:
sorry idol grade 8 lng ako eh sensya kana godbless
Which is the graph of y= -x + 2?
Answer:
Its A
Step-by-step explanation:
y intercept equal 2 so it must intersect at 2 on the y axis and it must go down because its a negative function
Lin’s second pan has a length of \frac{8}{3} inches, a width of \frac{15}{4} inches, and a height of \frac{3}{2} inches.
Answer:
15
Step-by-step explanation: so i did 8/3 x 15/4 x 3/2 and got 15
solve for x: x/-5+6≤2
Answer:
x ≥ 20
Step-by-step explanation:
hope this helps!
Answer:
x>= 20 or 20≤x
Step-by-step explanation:
Isolate x
Subtract 6 from both sides:
x/-5<=-4
Multiply both sides by -5, and switch the inequality sign bc u multiplied by a negative number:
x>= 20
Place these numbers in order from small to big. 35% , 36/100, 4/25, 0.85, 2.6, 0.1
Answer:
0.1, 4/25, 35%, 36/100, 0.85, 2.6
Step-by-step explanation:
What is the result when 9r^3 + 27x^2 + 11x +1 is divided by 3x + 1?
Answer:
the answer is 3x^2 + 8x + 1
Step-by-step explanation:
(I used x as the variable due to the invalid difference of variables in your question )
To find the correct answer, I had to use polynomial division.
(9 x 3 + 27 x 2 + 11 x + 1) / (3 x + 1)
= ( 3 x + 1 ) ( 3 x 2 + 8 x + 1 ) / (3 x + 1)
= 3 x 2 + 8 x + 1
someone pls hurry and help !
I will give brainiest to whoever answers correctly !!
Answer:
the material when you get a chance can you send me the material
Nike shoes are 45% off $80.
What will be the savings
on
the
tennis shoes ?
Answer:
You pay $44 / You're saving $36
Step-by-step explanation:
100 - 45 = 55
$80 x 0.55 = $44
helppppppppppppppppppppppppppppppppjhfyigcusfdcusVCOUVc
Answer:
use the app called msthway
Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your sample points.)
int 1 between 5 x/2+3^3*dx
Answer:
[tex]\mathbf{4 \lim \limits _{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n(n+4i)}{2n^3 +(n+4i)^3} \Big )}[/tex]
Step-by-step explanation:
Given integral:
[tex]\int ^5_1 \dfrac{x}{2+x^3} \ dx[/tex]
[tex]\mathbf{Using \ Riemann \ sums; \ we \ have: }[/tex]
[tex]\int ^b_a \ f(x) \ dx = \lim_{n \to \infty} \sum \limits ^n_{i =1} \ f( a + i \Delta x) \Delta x[/tex]
[tex]here; \ \Delta x = \dfrac{b-a}{n}[/tex]
∴
[tex]\int ^5_1 \dfrac{x}{2+x^3} \ dx = f(x) = \dfrac{x}{2+x^3}[/tex]
[tex]\implies \Delta x = \dfrac{5-1}{n} =\dfrac{4}{n}[/tex]
[tex]f(a + i \Delta x ) = f ( 1 + \dfrac{4i}{n})[/tex]
[tex]f( 1 + \dfrac{4i}{n}) = \dfrac{n^2 ( n+4i)}{2n^3 + (n + 4i)^3}[/tex]
[tex]\lim_{n \to \infty} \sum \limits ^n_{i=1} \ f(a + i \Delta x) \Delta x = \lim_{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n^2(n+4i)}{2n^3 +(n+4i)^3} \Big )\dfrac{4}{n}[/tex]
[tex]\mathbf{= 4 \lim \limits _{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n(n+4i)}{2n^3 +(n+4i)^3} \Big )}[/tex]
here’s the other one
Answer:
it is A
Step-by-step explanation:
The tape diagram represents the ratio of your monthly allowance to your friend's monthly allowance. The monthly allowances total $90. How much is each allowance?
you [][][][][]
friend[][][][]
Your monthly allowance and your friend's monthly allowance is $50 and $40 respectively.
From the given tape diagram, the ratio of your monthly allowance to your friend's monthly allowance is 5:4.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, 5+4=9
Now, your monthly allowance = 5/9 × 90
= 50
So, your friend's monthly allowance = 90-50 = 40
Therefore, your monthly allowance and your friend's monthly allowance is $50 and $40 respectively.
To learn more about the ratio visit:
brainly.com/question/13419413.
#SPJ2
What is the value of the expression (2/5+2/5)×3/10?
HELP
[tex]( \frac{2}{5} + \frac{2}{5} ) \times \frac{3}{10} [/tex]
[tex] \frac{4}{5} \times \frac{3}{10} [/tex]
[tex] \frac{6}{25} [/tex]
Decimal Form:
[tex]0.24[/tex]
HopeItHelps you
#CarryOnLearning
What value of P makes the equation true?
2.5 + 0.15p = 0.4p
p = ___
Step-by-step explanation:
2.5 + 0.15p = 0.4p
0.25p = 2.5 (subtract 0.15p on both sides)
p = 10 (multiply 4 on both sides)
Answer:
[tex]2.5 + 0.15p = 0.4p \\ 2.5 = 0.25p \\ p = \frac{2.5}{0.25} \\ \boxed{p = 10}[/tex]
10 is the right answer.
Find the measure of angle B
(9x+2) (5x-4)
Answer:
119
Step-by-step explanation:
[tex]due \: to \: Corresponding \: angles \\ (5x - 4) + (9x + 2) = 180 \\ 14x = 182 \\ x = 13 \\ \\ 9.13 + 2 = b \\ b = 119[/tex]
Answer:
In the given figure, we know that (angle B+angle C)=180°.
[tex](9x + 2) + (5x - 4) = 180 \\ 14x - 2 = 180 \\ 14x = 182 \\ \boxed{x = 13}[/tex]
Angle B = (9x+2) = (9×13+2) = (117+2) = 119°.
Solve the proportion ASAP help do both questions
Answer:
7. 4
8. 7
Step-by-step explanation:
7. [tex] \frac{1}{2} = \frac{x}{8} [/tex]
Cross multiply
[tex] 1*8 = x*2 [/tex]
[tex] 8 = 2x [/tex]
[tex] \frac{8}{2} = \frac{2x}{2} [/tex] (division property of equality)
[tex] 4 = x [/tex]
[tex] x = 4 [/tex]
8. [tex] \frac{3}{x - 3} = \frac{6}{8} [/tex]
Cross multiply
[tex] 3*8 = 6(x - 3) [/tex]
[tex] 24 = 6x - 18 [/tex]
[tex] 24 + 18 = 6x [/tex] (addition property of equality)
[tex] 42 = 6x [/tex]
Divide both sides by 6
[tex] 7 = x [/tex]
[tex] x = 7 [/tex]
The table shows the regular price and percent of discount for four items. Write the correct sale price for each item. Round to the nearest cent if necessary.
Answer:
Step-by-step explanation:
A. $154.20 * 0.65 = $100.23
B. $91.96 * 0.70 = $64.37
C. $47.60 * 0.75 = $35.70
D. $84.60 * 0.80 = $67.68
Teagan was building a fence around his lawn.
The area of his lawn was 36 sq. yds. His lawn is a
square. How much fencing will he need?
Step-by-step explanation:
36×2=72
he will need 18 inches fencing