# Get Busy – Probability

It is due on Sunday the 10th of March.

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7.9

Suppose that 5.000 sales invoices are separated into four strata. Stratum 1 contains 50 invoices, stratum 2 contains 500 invoices, stratum 3 contains 1,000 invoices and stratum 4 contains 3.450 invoices. a sample of 500 sales invoices is needed.

a) What type of sampling should you do? Why?

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b) Explain how you would carry out the sampling according to the method sated in (a)

c) Why is the sampling in (a) not simple random sampling?

7.21

Time spent using e-mail per session is normally distributed, with µ = 8 minutes and σ = 2 minutes. If you select a random sample of 25 sessions,

a) What is the probability the sample mean is between 7.8 and 8.2 minutes?

b) What is the probability that the sample mean is between 7.5 and 8 minutes?

c) If you select a random sample of 100 sessions, what is the probability that the sample mean is between 7.8 and 8.2 minutes?

d) Explain the difference in the results of (a) and (c).

7.23

In a random sample of 64 people, 48 are classified as “successful.”

a) Determine the sample proportion, p, of “successful” people.

b) If the population proportion is 0.70, determine the standard error of the proportion.

7.25

The following data represent the responses (Y for yes and N for no) from a sample of 40 college students to the question “Do you currently own shares in any stock?”

N N Y N N Y N Y N Y N NY N Y Y N N N Y

N Y N N N N Y N N Y Y N N N Y N N Y N N

a) Determine the sample proportion, p, of college students who own shares of stock.

b) If the population proportion is 0.30, determine the standard error of the proportion.

7.29

Companies often make flextime scheduling available to help recruit and keep women employees who have children. Other workers sometimes view these flextime schedules as unfair. An article in USA Today indicates that 25% of male employees state that they have to pick up the slack for moms working flextime schedules (data extracted from D. Jones, “Poll Finds Resentment of Flextime,”

www.usatoday.com

, May 11, 2007). Suppose you select a random sample of 100 male employees working for companies offering flextime.

a) What is the probability that 25% or fewer male employees will indicate that they have to pick up the slack for moms working flextime?

b) What is the probability that 20% or fewer will indicate that they have to pick up the slack for moms working flextime?

c) If a random sample of 500 is taken, how does this change your answers to (a) and (b)?

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