Statistics Chapter 6

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. 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 standard deviation of X is 1.27. Interpret this value.

• The number of computers in a randomly selected household is within 1.27 of the mean.

• The number of computers in a randomly selected household is exactly 1.27 from the mean.

• The number of computers in a randomly selected household is 1.27, on average.

• The number of computers in a randomly selected household is typically 1.27 from the mean.

• The average number of computers in a randomly selected household is typically 1.27 from the mean.

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric

A spinner has 5 equally-sized regions (blue, green, red, orange, and yellow). If you spin the spinner 20 times, what is the probability that the spinner lands on blue at most 5 times?

• Approximately 0

• 0.370

• 0.630

• 0.804

• 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

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

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?

• n = 10, p = 0.5

• n = 40, p = 0.88

• n = 100, p = 0.2

• n = 100, p = 0.99

• n = 1000, p = 0.003

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.

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric