A random sample of 125 monthly balances for holders of a particular credit card indicated that the sample skewness was 0.55 and the sample kurtosis was 2.77. Test the null hypothesis that the population distribution is normal.

In a period of 100 minutes there were a total of 190 arrivals at a highway toll booth. The accompanying table shows the frequency of arrivals per minute over this period. Test the null hypothesis that the population distribution is Poisson.

$$\begin{array}{lccccc} \hline \text { Number of arrivals } & & & & & \\ \text { in minutes } & 0 & 1 & 2 & 3 & 4 \text { or more } \\ \hline \text { Observed frequency } & 10 & 26 & 35 & 24 & 5 \\ \hline \end{array}$$

The number of times a machine broke down each week was observed over a period of 100 weeks and recorded in the accompanying table. It was found that the average number of breakdowns per week over this period was 2.1. Test the null hypothesis that the population distribution of breakdown is Poisson.

$$\begin{array}{lcccccc} \hline \text { Number of breakdowns } & 0 & 1 & 2 & 3 & 4 & 5 \text { or more } \\ \hline \text { Number of weeks } & 10 & 24 & 32 & 23 & 6 & 5 \\ \hline \end{array}$$

A random sample of statistics professors was asked to complete a survey including questions on curriculum content, computer integration, and software preferences. Of the 250 responses, 100 professors indicated that they preferred software package M and 80 preferred software package E, whereas the remainder were evenly split between preference for software package S and software package P. Do the data indicate that professors have a preference for any of these software packages?

A random sample of 150 residents in one community was asked to indicate their first preference for one of three television stations that air the 5 p.m. news. The results obtained are shown in the following table. Test the null hypothesis that for this population their first preferences are evenly distributed over the three stations.

$$\begin{array}{lccc} \hline \text { Station } & \text { A } & \text { B } & \text { C } \\ \hline \text { Number of first preferences } & 47 & 42 & 61 \\ \hline \end{array}$$

You have a set of 36 flash cards numbered from 1 to 36. A card is chosen at random. Find the odds in favor of, and the odds against, each selection. prime number

Use the theoretical method to determine the probability of the following outcomes and events. State any assumptions that you make.

Drawing a black card (club or spade) from a standard deck of cards

Two cards from a standard deck of 52 playing cards are successively drawn at random with replacement. Find the probability that (a) both cards are kings and (b) one card is a king and the other is a heart.

Use the method of your choice to determine the following probabilities.

Drawing three spades in a row from a standard deck of cards when the drawn card is returned to the deck each time

Emily wants to buy a tablecloth to cover a square card table. She knows the tabletop has an area of 9 square feet. What are the minimum dimensions of the tablecloth Emily needs?

A department store issues its own credit card, with an interest rate of 2% per month. Explain why this is not the same as an annual rate of 24%. What is the effective annual rate?

Ten cards numbered 1 through 10 are mixed together and then one card is drawn. Find the probability of the event. Write the answer as a fraction, percent, and decimal: P(less than 5)

Use the method of your choice to determine the following probabilities.

Drawing three queens in a row from a standard deck of cards when the drawn card is not returned to the deck each time

Suppose you have 4 baseball cards, and you asked a friend to choose 3 of them. How many different three-card combinations could your friend choose?