1)In the binomial probability distribution, let the number of trials be n = 3, and let the probability of success be p = 0.2662. Use a calculator to compute the following.

(a) The probability of two successes. (Round your answer to three decimal places.)

(b) The probability of three successes. (Round your answer to three decimal places.)

(c) The probability of two or three successes. (Round your answer to three decimal places.)

2) Approximately 65% of all marketing personnel are extroverts, whereas about 50% of all computer programmers are introverts. (Round your answers to three decimal places.)

(a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts?

What is the probability that 5 or more are extroverts?

What is the probability that all are extroverts?

(b) In a group of 4 computer programmers, what is the probability that none are introverts?

What is the probability that 2 or more are introverts?

What is the probability that all are introverts?

3) Jim is a 60-year-old Anglo male in reasonably good health. He wants to take out a $50,000 term (that is, straight death benefit) life insurance policy until he is 65. The policy will expire on his 65th birthday. The probability of death in a given year is provided by the Vital Statistics Section of the Statistical Abstract of the United States (116th Edition).

x = age 60 61 62 63 64

P(death at this age) 0.01048 0.01312 0.01630 0.02044 0.02221

Jim is applying to Big Rock Insurance Company for his term insurance policy.

(a) What is the probability that Jim will die in his 60th year? (Enter your answer to five decimal places.)

Using this probability and the $50,000 death benefit, what is the expected cost to Big Rock Insurance? (Round your answer to two decimal places.)

$

(b) Repeat part (a) for years 61, 62, 63, and 64. (Round your answers to two decimal places.)

Year Expected Cost

61 $

62 $

63 $

64 $

What would be the total expected cost to Big Rock Insurance over the years 60 through 64? (Round your answer to two decimal places.)

$

(c) If Big Rock Insurance wants to make a profit of $700 above the expected total cost paid out for Jim's death, how much should it charge for the policy? (Round your answer to two decimal places.)

$

(d) If Big Rock Insurance Company charges $5000 for the policy, how much profit does the company expect to make? (Round your answer to two decimal places.)

4) Barbara is a research biologist for Green Carpet Lawns. She is studying the effects of fertilizer type, temperature at time of application, and water treatment after application. She has three fertilizer types, two temperature zones, and two water treatments to test. Determine the number of different lawn plots she needs in order to test each fertilizer type, temperature range, and water treatment configuration.

5) There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor; position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position. There are 10 candidates qualified for all three of the positions. Determine the number of different ways the positions can be filled by these applicants.

6) John runs a computer software store. Yesterday he counted 125 people who walked by the store, 51 of whom came into the store. Of the 51, only 21 bought something in the store.

(a) Estimate the probability that a person who walks by the store will enter the store. (Round your answer to two decimal places.)

(b) Estimate the probability that a person who walks into the store will buy something. (Round your answer to two decimal places.)

(c) Estimate the probability that a person who walks by the store will come in and buy something. (Round your answer to two decimal places.)

(d) Estimate the probability that a person who comes into the store will buy nothing. (Round your answer to two decimal places.)

7) In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set.

7, 5, 6, 15, 5

(a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to one decimal place.)

(b) Add 3 to each data value to get the new data set 10, 8, 9, 18, 8. Compute s. (Enter your answer to one decimal place.)

(c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?

Adding the same constant c to each data value results in the standard deviation remaining the same.

Adding the same constant c to each data value results in the standard deviation increasing by c units.

Adding the same constant c to each data value results in the standard deviation decreasing by c units.

There is no distinct pattern when the same constant is added to each data value in a set.

8) What are the big corporations doing with their wealth? One way to answer this question is to examine profits as percentage of assets. A random sample of 50 Fortune 500 companies gave the following information. (Source: Based on information from Fortune 500, Vol. 135, No. 8.) Estimate the sample mean, sample variance, and sample standard deviation for profit as percentage of assets. (Enter your answers to one decimal place.)

Profit as percentage of assets 8.6-12.5 12.6-16.5 16.6-20.5 20.6-24.5 24.6-28.5

Number of companies 11 15 3 6 15

x

s2

s