# MATH 251 Community College of Philadelphia Normal Distribution Statistics Questions

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1. Let X be a standard normal random variable. Find P(X < 0). Express your answer as a decimal.

2. Let X be a standard normal random variable. Find P(X ? -2.27). Express your answer as a decimal.

3. Let X be a standard normal random variable. Find P(X > 2.82). Express your answer as a decimal.

4. Let X be a standard normal random variable. Find P(-1.20 < X < 1.74). Express your answer as a decimal.

5. Assume that thermometer readings are normally distributed with a mean of 0 degrees Celsius and a standard deviation of 1 degree Celsius. A thermometer is randomly selected and tested. Find the temperature reading that separates the bottom 93.7% from the top 6.3%. Round your answer to the nearest hundredth.

6. Assume that thermometer readings are normally distributed with a mean of 0 degrees Celsius and a standard deviation of 1 degree Celsius. A thermometer is randomly selected and tested. Find the temperature reading that separates the bottom 40.9% from the top 59.1%. Round your answer to the nearest hundredth.

7. 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?

8. A survey by the National Retail Federation found that women spend on average \$146.21 for the Christmas holidays. Assume the standard deviation is \$29.44. Find the percentage of women who spend less than \$160.00. Assume the variable is normally distributed. Express the answer in the form of a percentage (do not include % sign in your answer). Round your answer to the nearest hundredth.

9. Each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds. If a household is selected at random, find the probability of its generation between 27 and 31 pounds per month. Assume the variable is normally distributed. Express your answer as a percentage. (do not include % sign in your answer). Round your answer to the nearest hundredth.

10. The national average SAT score (for Verbal and Math) is 1028. If we assume a normal distribution with standard deviation 92, what is the probability that a randomly selected score exceeds 1200? Express your answer as a decimal. Round your answer to the nearest hundredth.

11. To qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify. Assume the test scores are normally distributed and that only whole number scores are possible.

12. The average price of a personal computer is \$949. If the computer prices are normally distributed with a standard deviation of \$100, the least expensive 10% of personal computers cost less than what amount? Round your answer to the nearest dollar.

https://archive.org/details/Elementary_Statistics_A_Step_by_Step_Approach_7th_Edition_by_Allan_G._Blumanheres a link to the free online version

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