Question 1

Let

Z

be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places.

=P>Z1.04

=PZ1.61

=P<0.78<Z1.90

Question 2

Let

Z

be a standard normal random variable. Use the calculator provided, or this table, to determine the value of

c

.

=PZc0.8729

Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

Question 3

Let

Z

be a standard normal random variable. Use the calculator provided, or this table, to determine the value of

c

.

=PcZ0.870.1494

Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

Question 5

Suppose that the heights of adult women in the United States are normally distributed with a mean of

64

inches and a standard deviation of

2.2

inches. Jennifer is taller than

80%

of the population of U.S. women. How tall (in inches) is Jennifer? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

Question 6

Suppose that the lifetimes of TV tubes are normally distributed with a standard deviation of

1.2

years. Suppose also that exactly

40%

of the tubes die before

4

years. Find the mean lifetime of TV tubes. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

years

Question 7

Suppose that the time required to 1040R tax form is normally distributed with a mean of

90

minutes and a standard deviation of

15

minutes. What proportion of 1040R tax forms will be completed in at least

85

minutes? Round your answer to at least four decimal places.

Question 8

A brokerage survey reports that

27%

of all individual investors have used a discount broker (one that does not charge the full commission). If a random sample of

90

individual investors is taken, approximate the probability that fewer than

26

have used a discount broker. Use the normal approximation to the binomial with a correction for continuity.

Round your answer to at least three decimal places. Do not round any intermediate steps.

Question 9

Alcohol withdrawal occurs when a person who uses alcohol excessively suddenly stops the alcohol use. Studies have shown that the onset of withdrawal is experienced a mean of

39.5

hours after the last drink, with a standard deviation of

19

hours. A sample of

36

people who use alcohol excessively is to be taken. What is the probability that the sample mean time between the last drink and the onset of withdrawal will be

38.8

hours or more?

Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Question 10

In a memory test, the test subjects are shown

300

objects and are asked after two hours to name the objects. The historical records show that test subjects remember

75%

of the objects after two hours.

a.Find the mean of

p

, where

p

is the proportion of objects that are remembered by a test subject.

b.Find the standard deviation of

p

.

c.Compute an approximation for

P>p0.72

, which is the probability that more than

72%

of the objects are remembered by a test subject. Round your answer to four decimal places.

a.b.c.