**Question 6 **

Consider the following results for two samples randomly taken from two normal populations with equal variances.

Sample I | Sample II | ||

Sample Size | 28 | 35 | |

Sample Mean | 48 | 44 | |

Population Standard Deviation | 9 | 10 |

a. Develop a 95% confidence interval for the difference between the two population means.

b. Is there conclusive evidence that one population has a larger mean? Explain.

**Question 13 **

A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks to their clients. A sample of the sales for 36 days revealed average daily sales of $200,000. Assume that the standard deviation of the population is known to be $18,000.

a. Provide a 90% confidence interval estimate for the average daily sale.

b. Provide a 99% confidence interval estimate for the average daily sale.

**uestion 21 **

The weight of a .5 cubic yard bag of landscape mulch is uniformly distributed over the interval from 38.5 to 41.5 pounds.

What is the probability that a bag will weigh less than 41 pounds?

**Question 24 **

The weekly earnings of fast-food restaurant employees are normally distributed with a mean of $395. If only 10.2% of the employees have a weekly income of more than $422.94, what is the value of the standard deviation of the weekly earnings of the employees?

**Question 25 **

An investment advisor recommends the purchase of shares in Infogenics, Inc. He has made the following predictions:

P(Stock goes up 20% | Rise in GDP) = .6

P(Stock goes up 20% | Level GDP) = .5

P(Stock goes up 20% | Fall in GDP) = .4

An economist has predicted that the probability of a rise in the GDP is 20%, whereas the probability of a fall in the GDP is 40%.

What is the probability that the stock will go up 20%?

**Question 27 **

An investment advisor recommends the purchase of shares in Infogenics, Inc. He has made the following predictions:

P(Stock goes up 20% | Rise in GDP) = .6

P(Stock goes up 20% | Level GDP) = .5

P(Stock goes up 20% | Fall in GDP) = .4

An economist has predicted that the probability of a rise in the GDP is 20%, whereas the probability of a fall in the GDP is 40%.

We have been informed that the stock has gone up 20%. What is the probability of a rise or fall in the GDP?