Statistics and Probability with Application

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is approximately Normal with mean $360 and standard deviation $50. The least profitable 10% of days have a profit of at most how many dollars?

• $244

• $296

• $370

• $424

• $476

Which of the following random variables is discrete?

• The number of shots made in 10 free-throw attempts.

• The weight of a rhinoceros.

• The species of an insect.

• The length of a needle on a saguaro cactus.

• None of the variables above are discrete.

A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the given distribution. The expected value of X is E(X) =

• 0.40

• 1.00

• 1.45

• 1.66

• 2.50

A marketing survey compiled data on the number of personal computers in households. X = the number of computers in a randomly-selected household. If you were to randomly select households, what is the probability it would take exactly 8 selections to find one with 5 computers?

• Approximately 0

• 0.02

• 0.03

• 0.32

• Approximately 1

The number of DVDs rented daily at DVD rental machine has a mean of 134 with a standard deviation of 32.

Select two days at random and find the difference in the number of DVDs rented on the two days. What are the mean and standard deviation of the difference in the number of DVDs rented?

• Mean = 0, Standard Deviation = 0

• Mean = 0, Standard Deviation = 64

• Mean = 0, Standard Deviation = 45

• Mean = 92, Standard Deviation = 32

• Mean = 134, Standard Deviation = 32

The number of DVDs rented daily at DVD rental machine has a mean of 134 with a standard deviation of 32.

The cost of the electricity to keep the DVD rental machine on is $1.45 per day. Each DVD rental increases the electricity cost by $0.02. What are the mean and standard deviation of the electricity cost per day?

• Mean = $4.13, Standard Deviation = $0.64

• Mean = $4.13, Standard Deviation = $1.77

• Mean = $4.13, Standard Deviation = $2.09

• Mean = $2.68, Standard Deviation = $0.64

• Mean = $2.68, Standard Deviation = $2.09

Which of the following random variables is geometric?

• The number of times I have to roll a die to get two 6s.

• The number of cards I deal from a well-shuffled deck of 52 cards until I get a heart.

• The number of digits I read in a randomly selected row of the random digits table until I find a 7.

• The number of 7s in a row of 40 random digits.

• The number of 6s I get if I roll a die 10 times.

Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that the hospital’s capacity will be exceeded?

• 0.011

• 0.965

• 0.035

• 0.989

• 0.092

The weight of tomatoes chosen at random from a bin at the farmer’s market follows a Normal distribution with mean = 10 ounces and standard deviation  = 1 ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T is

• Normal, with mean 10 ounces and standard deviation 1 ounce.

• Normal, with mean 40 ounces and standard deviation 2 ounces

• Normal, with mean 40 ounces and standard deviation 4 ounces

• binomial, with mean 40 ounces and standard deviation 2 ounces

• binomial, with mean 40 ounces and standard deviation 4 ounces.

The number of calories in a 1-ounce serving of a certain breakfast cereal is a random variable with mean 110 and standard deviation 10. The number of calories in a cup of whole milk is a random variable with mean 140 and standard deviation 12. For breakfast, you eat 1 ounce of the cereal and 1/2 cup of whole milk. Let T be the random variable that represents the total number of calories in this breakfast. The standard deviation of T is...

• 22

• 16

• 15.62

• 11.66