Probability & Random Variables

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

• $370

• $476

• $296

• $424

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 are discrete.

Let X represent the score earned by students from Central High School on the AP Statistics exam. The table shows the probability distribution of X. Find P(X = 5).

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) =

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.

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 weight of tomatoes chosen at random from a bin at the farmer’s market follows a normal distribution with mean of 10 ounces and standard deviation of 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 weights of Mu Candy Bars are approximately normally distributed with a mean of 8.3 oz and a standard deviation of 0.47 oz. What is the probability, to four decimal places, that the total weight of two randomly selected candy bars is more than 18 oz?

Mr. Feeny keeps a record of the number of high school students (X) who are late to school each day. A probability distribution of the school records are displayed. What is the standard deviation of the number of high school students who are late to school, the nearest hundredth?

A recent study showed that 60% of all US students say they "Love Statistics!" In a random sample of 5 students, what is the probability that at least one student "Loves Statistics"? Round to four decimal places.