Expected Value and Standard Deviation

The quality control manager at a factory records the number or equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Which of the following is the best interpretation of the standard deviation?

• The number of breakdowns on a randomly selected day is expected to be 0.28.

• The number of breakdowns on a randomly selected day will by 0.28 away from the mean.

• The average number of breakdowns per day for a random sample of days is expected to be 0.28

• On average, the number of breakdowns per day varies from the mean by about 0.28.

• The number of breakdowns per day for a random sample of days is expected to be 0.28 away from the mean.

Expected value is the ________ one can expect over many repeated trials.

• best outcome

• total combination of outcomes

• average outcome

• worst outcome

Which of the following best describes how to calculate expected value?

• Add each possible outcome together, and multiply the sum by the probability of the least likely outcome.

• Multiply each possible outcome by its probability, and add each product together.

• Multiply each possible outcome by itself, and add each product together.

• Add each probability together, and multiply it by the sum of each possible outcome.

Choose an American household at random and let the random variable 𝑋 be the number of cars (including SUVs and light trucks) they own. The standard deviation of 𝑋 is 𝜎𝑥 = 1.08. If many households were selected at random, which of the following would be the best interpretation of the value 1.08?

• The number of cars would be at most 1.08 from the mean.

• The number of cars would be within 1.08 from the mean about 68% of the time.

• The mean number of cars would be about 1.08.

• The number of cars would typically be about 1.08 from the mean.

The number of sweatshirts a vendor sells daily has the following probability distribution.

What is the expected value?

Find the value of c

• 0.8

• 0.2

• 0.3

• 0.1

The table above shows a television station's advertisement sales. The distribution of sales for one 24-hour day is given. Solve for the mean. Round to the nearest hundredth.

• 31.8

• 15.68

• 0.20

• 1.00

What is the mean of the data?

A discrete random variable X has the probability distributions shown in the table. Find the value of k. (Remember that a valid probability distribution must add up to 1)

• 1/3

• 7/12

• 1/12

• 1/4

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5.  What proportion of weeks would you expect to have less than 5 accidents?

• 0.6915

• 0.1762

• 0.8238

• -0.93