Expected Values and Standard Deviation

For a certain type of computer, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours.

In a city, it is estimated that the maximum temperature for the thirty days of June is normally distributed with a mean of 23 degrees and a standard deviation of 5 degrees. Calculate the number of days in this month in which it is expected to reach a maximum temperature between 21 and 27 degrees.

For Mrs. V: mean = 55 and standard deviation = 19 For Mr. T: mean = 33 and standard deviation = 10.5 Mary Beth is very proud of the score of 80 that she earned in Mrs. V's class. Albert is equally proud of the score of 42 he earned in Mr. T's class. Who has the better score?

For Mrs. V: mean = 55 and standard deviation = 19
For Mr. T: mean = 33 and standard deviation = 10.5

What percent of students scored 80 or higher in Mrs. V's class? Round your answer to the nearest tenth, do not put a percent sign.

(a)  

Find the mean (expected value) of the probability distribution.

Data was compiled and the number of goals for a hockey team per game and the corresponding probabilities are given below. If this hockey team plays an 82-game season, what is the expected cumulative goal total for the next season?

You are considering a game where you pay $$5 to roll a die with the promise of receiving$$ 10 if you roll a 6. What is the expected value of playing this game?

In a lottery, 1000 tickets are sold for $$1 each. One winning ticket is drawn, and the prize is$$ 500. What is the expected value of buying one ticket?

Data was compiled and the number of goals for a hockey team per game and the corresponding probabilities are given below. If this hockey team plays an 82-game season, what is the expected cumulative goal total for the next season?

You have a game where you can draw one card from a standard deck of 52 cards. If you draw a heart, you win $5; otherwise, you win nothing. What is the expected value of your winnings?