math 7

IMPORTANT: In any question, if there is a calculation, first provide the formula and then show your calculations for your answers.

Please, provide your answers under each question.

Data files can be found in the D2L.

Question 1 (Short Exercise 1 in the book) (5*1+2=7 points)

A uniform distribution is defined over the interval from 6 to 10.

a. What are the values for a and b?

b. What is the mean of this uniform distribution?

c. What is the standard deviation?

d. Show that the total area is 1.00.

e. Find the probability of a value more than 7.

f. Find the probability of a value between 7 and 9. (2 points)

Question 2 (Short Exercise 9 in the book) (3*2=6 points)

The mean of a normal probability distribution is 500; the standard deviation is 10.

a. About 68% of the observations lie between what two values?

b. About 95% of the observations lie between what two values?

c. Practically all of the observations lie between what two values?

Question 3 (Short Exercise 14 in the book) (3*2=6 points)

A normal population has a mean of 12.2 and a standard deviation of 2.5.

a. Compute the z value associated with 14.3.

b. What proportion of the population is between 12.2 and 14.3? (Appendix B.3)

c. What proportion of the population is less than 10.0?

Question 4 (Short Exercise 18 in the book) (3*2=6 points)

A normal population has a mean of 80.0 and a standard deviation of 14.0.

a. Compute the probability of a value between 75.0 and 90.0.

b. Compute the probability of a value of 75.0 or less.

c. Compute the probability of a value between 55.0 and 70.0.