Paleomagnetic studies of Canadian volcanic rock known as the Carmacks Group have recently been completed. The studies revealed that the northward displacement of the rock units has an approximately normal distribution with a standard deviation of 500 kilometers (Canadian Journal of Earth Sciences, Vol. 27, 1990). One group of researchers estimated the mean displacement at 1,200 kilometers, whereas a second group estimated the mean at 1,000 kilometers.

Required:
a. Assuming the mean is 1500 kilometers, what is the probability of a northward displacement of less than 500 kilometers?
b. Assuming the mean is 1200 kilometers, what is the probability of a northward displacement of less than 500 kilometers?
c. If, in fact, the northward displacement is less than 500 kilometers, which is the more plausible mean, 1200 or 1500 kilometers?

Answer:

a) 0.0228 = 2.28% probability of a northward displacement of less than 500 kilometers

b) 0.0808 = 8.08% probability of a northward displacement of less than 500 kilometers

c) 1200 kilometers, because in this case, the will be a higher probability of a northward displacement that is less than 500 kilometers.

Step-by-step explanation:

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 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.

Standard deviation of 500 kilometers

This means that [tex]\sigma = 500[/tex]

a. Assuming the mean is 1500 kilometers, what is the probability of a northward displacement of less than 500 kilometers?

Mean of 1500 km means that [tex]\mu = 500[/tex]

The probability is the pvalue of Z when X = 500. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{500 - 1500}{500}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.0228 = 2.28% probability of a northward displacement of less than 500 kilometers.

b. Assuming the mean is 1200 kilometers, what is the probability of a northward displacement of less than 500 kilometers?

Now [tex]\mu = 1200[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{500 - 1200}{500}[/tex]

[tex]Z = -1.4[/tex]

[tex]Z = -1.4[/tex] has a pvalue of 0.0808

0.0808 = 8.08% probability of a northward displacement of less than 500 kilometers.

c. If, in fact, the northward displacement is less than 500 kilometers, which is the more plausible mean, 1200 or 1500 kilometers?

1200 kilometers, because in this case, the will be a higher probability of a northward displacement that is less than 500 kilometers.

Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics. Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized, continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal.) The results were as follows:

Duration of Exposure
< 1 1 to < 5 >= 5
Diseased 12 10 18
Sensitized 14 18 13
Normal 66 142 210

Required:
a. Compute the expected frequencies of diseased workers.
b. Compute the expected frequencies of sensitized workers.
c. How many degrees of freedom are there?

I WILL GIVE BRAINLIEST !!!What is the product of 4 and 7?
7
O
o
8 9
14
9
14
7
8

Find legit BD

I need help for my assignment

Help Me Please.............................(7)

Dan is randomly selecting an outfit to wear to school. He can choose from 3 shirts: blue striped, red striped, or white. He
can choose from 3 pairs of shorts: tan, blue, or plaid.
Determine whether each statement is true or false.
Select True or False for each statement.
The probability that Dan chooses a striped shirt and a pair of tan shorts is
O True
o
False
There are 6 possible outcomes in the sample space.
O
True
O
False
The probability that Dan chooses a striped shirt and a pair of blue shorts is
o
True
O False
There are 2 ways to choose a red striped shirt and a pair of tan shorts.
O True
O False

Solve the equation by completing the square.
a2 - 14a - 32 = 0

Explain the difference between a percent and a unit rate.

I have to do a math test what is 8 + (7 + 1) 2 ÷ 4 ⋅

(X8.6.PS-12
Question Help
A circular flower bed is 20 m in diameter and has a circular sidewalk around it that is 2 m wide.
Find the area of the sidewalk in square meters. Use 3.14 for it.
The area of the sidewalk is m2.
(Round to the nearest whole number as needed.)
Enter your answer in the answer box and then click Check Answer.
Clear All
Check Answer
All parts showing

Draw a line through the origin with a slope of 3/2

the ages of six boys are given as 12 years 3 months, 18 years, 13 years 7 months, 17 years 2 months 15 years and 14 years respectively. what is their average age? ​

Kenji walks 44 feet in 10 seconds. At this rate, how many miles does Kenji walk in an hour? Show your work. (1 mile 5 5,280 feet) (make it simple)

Pls help. Im so lost.

Find the lengths of the missing side. Round your answer to the nearest tenth

Pineapple Corporation (PC) maintains that their cans have always contained an average of 12 ounces of fruit. The production group believes that the mean weight has changed. They take a sample of 15 cans and find a sample mean of 12.05 ounces and a sample standard deviation of .08 ounces. What conclusion can we make from the appropriate hypothesis test at the .01 level of significance

Can someone please help me?

WILL MARK BRAINLIEST!! Just help me out with number 2 please. :)

Here is an inequality: -2x > 10.
1. List some values for x that would make this inequality true.
Answer: Any negative number above -5, like -6, -7, etc.

2. How are the solutions to the inequality -2x ≥ 10 different from the solutions to
-2x > 10? Explain your reasoning.

Rotational symmetry of 2D shapes
Choose all that apply
​

Priya rewrites the expression 8y−24 as 8(y−3). Han rewrites 8y−24 as 2(4y−12). Are Priya's and Han's expressions each equivalent to 8y−24? Explain your reasoning

Solve the following question:
 
Q1: A family has booked a long holiday in Skragness, where the probability of rain on any particular day is 0.3. 
a) Find the probability that the first day to rain will be on the third day of their holiday.
b) Find the probability chance that it will not rain for the first 2 weeks of their holiday.
 
[hint:  X~Geo(0.3)  a) P(X=__), b) P(X<__)]
 
Q2: If G~B(42, 7/12)
a) Find E(G) and Var(G) giving your answer as a fraction or mixed number
 
b*) Find P(G=20) correct to 3 significant figures.

The diameter of the circle shown below is 12m. What is the area of the circle

WILL GIVE BRAINLIST PLS HELP Find z. Just write the number. Answer should be a whole number.

If the temperature was -24 degrees yesterday. If the temperature is 5 degrees now. What was the temperature change

The show has a large display board where visitors are encouraged to pin up their pictures during an even, it measures:
3.6 m
1.8 m

How many 6 cm by 6 cm pictures could fit on the wall?​

If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.

Mr. Brown purchased 5.75 pounds of chicken that cost $2.40 per pound How much change should he receive if he pays with a $20 bill? a)​

NO LINKS (QUESTION BELOW)

I Need help plz will give brainlyist for the correct answer

35% of students enrolled in collage are freshmen. if the total enrollment of the collage is 2800, how many of the students are freshmen?

Find the vertex of the parabola y=2x^2+10x+8​