Homework Answers

11. Find z if the standard normal-curve area

a) between 0 and z is 0.4726;

b) to the left of z is 0.9868;

c) to the left of z is 0.3085;

d) between -z and z is 0.9282

12. If a random variable has the normal distribution with \mu = 82:0 and
\sigma = 4:8, nd the probabilities that it will take on a value

a) less than 89.2;

b) greater than 78.4;

c) between 83.2 and 88.0;

d) between 73.6 and 90.4.

13. If the time to assemble an \easy to assemble" computer desk from a

kit is a random variable having the normal distribution with \mu = 55:8
minutes and \sigma = 12:2 minutes, what are the probabilities that this

kind of desk can be assembled in

a) less than 49.7 minutes;

b) anywhere from 61.9 and 74.1 minutes;

c) more than 86.3 minutes?

14. With reference to Exercise 13, for what length of time is the probability

0.90 that one can assemble the desk in that many minutes or less?

8. A quality control engineer wants to check whether, in accordance with specication, 90% of products shipped are in perfect working condition. To this end, she randomly selects 12 items from each lot ready to be shipped and passes the lot only if all 12 are in perfect working condition. If one or more are not in perfect working condition, she holds the lot for a complete inspection. Find the probability that she will commit the error of

a) holding a lot for a complete inspection even though 90% of the items are in perfect working condition;

b) letting a lot pass through even though only 80% of the items are in perfect working condition;

10. Find the area under the standard normal curve that lies

a) between z = 0 and z = 0.87;

b) between z = -1.66 and z = 0;

c) to the right of z = 0.48;

d) to the right of z = -0.27;

e) to the left of z = 1.30;

f) between z = 0.45 and z = 1.23;

h) between z = 1.15 and z = 1.23;

i) between z = -1.35 and z = 1.35

j) between z = -2.35 and z = -1.46.

4. Explain in each case why the given equation cannot serve as the probability density function of a random variable that takes on values on the interval from 0 to 5:

a) f(x) = 1/10 (x - 4);

b) f(x) = 1/50 (x + 1).

5. A doctor knows from experience that 10% of of the patients to whom

he prescribes a certain blood pressure medication will have undesirable

side effects. Calculate the probability that of the 10 randomly selected

patients:

a) none will have undesirable side effects;

b) exactly 4 patients will have undesirable side effects;

c) at most 3 will have undesirable side effects;

d) at least 3 will have undesirable side effects.

6. Refer to Exercise 5. What is the expected number of patients with

undesirable side effects. What is the standard deviation of the number

of patients with undesirable side effects.