The average price for an acre of land is $20,000 with a standard deviation of $2500.  What is the probability that a randomly selected plot of land will sell for more than $23,000?

Insurance companies make bets. They bet that you’re going to live a long life. An insurance company offers a “death and disability” policy that pays average of $10,000 when you die with a standard deviation of $1,000 or pays average $5000 if you are permanently disabled with standard deviation of $1,000.  Assuming the distribution of the policy payout is normal. What percentage of pay will lie between payout of $7,000 and $9,000 when you die? What percentage of the payout will lie below $7,500 if you are permanently disabled? What percentage of the policy will lie above $8,100 when you die?

One year, the distribution of salaries for professional sports players had mean $1.6 million and standard deviation $0.81 million. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players that year exceeded $1.7 million. Round your answer to nearest ten-thousandth.

Mario's weekly poker winnings have a mean of $353 and a standard deviation of $67. Last week he won $185. How many standard deviations from the mean is that?

Suppose you pay $500 per year to insure your car worth $10,000. The probability that you get in an accident, totaling the car, in any year is 0.001. Find your standard deviation for the insurance. Round your answer to the nearest dollar.

Cody took his first physics exam and scored an 80. The population mean for this exam is 70, and the standard deviation is 5. What is the probability of selecting a person with a score greater than Cody’s?

A successful basketball player has a height of 6 feet 11 ​inches, or 211 cm. Based on statistics from a data​ set, his height converts to the z score of 5.17. How many standard deviations is his height above the​ mean?

The NJ Department of Health has reported the average life span of NJ residents is 81 years. If the standard deviation is σ = 4 years, what is the probability of a person living to at least 92 years of age?

You draw a card from a deck. If you get a red​ card, you win nothing. If you get a​ spade, you win ​$6. For any​ club, you win ​$12 plus an extra ​$20 for the ace of clubs. Find the standard deviation of the amount you might win drawing a card.

Given that the mean and standard deviation are $24 and $3. Calculate the variance.