Standard Deviation and Expected Value of Random Variables

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 mean of T is...

• 110

• 140

• 180

• 195

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

It turns out that 25 seniors at Fashionable High School took both the AP Statistics exam and the AP Spanish Language exam. The mean score on the Statistics exam for the 25 seniors was 2.4 with standard deviation of 0.6, and the mean score on the Spanish Language exam was 2.65 with a standard deviation of 0.55. We want to combine the scores into a single score. What are the correct mean and standard deviation of the combined scores?

• 5.05; 1.15

• 5.05; 1.07

• 5.05; 0.66

• 5.05; 0.81

• 5.05; You cannot determine the standard deviation from this information.

The following table gives the probabilities of various outcomes for a gambling game. What is the player's expected return on a bet of $1?

• $0.05

• -$0.60

• -$0.05

• -$0.10

• You can't answer this question since this is not a complete probability distribution.

A binomial event has n = 60 trials. The probability of success on each trial is 0.4. Let X be the count of successes of the event during the 60 trials. What are mean X and standard deviation X?

• 24; 3.79

• 24; 14.4

• 4.9; 3.79

• 4.9; 14.4

The probability of x, the number of tires needing replacement on a randomly selected automobile checked at a certain inspection station is given in the following table. What is the standard deviation of X?

• 1.2

• 2.52

• 1.58

The number of vehicles leaving a highway at a certain exit during a particular time period has a distribution that is approximately normal with mean value 500 and standard deviation 75. What is the probability that the number of cars exiting during this period is at least 650?

• 0.977

• 0.023

• 0.477

• 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

• 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 radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling at more than 100 km/hr?

• 0.4391

• 1.368

• 0.675

• 0.1587