# Probability of normal distribution problem

1. Find the area under the Normal Distribution from the mean to a z-score of -2.07.

2. Find the z-score that corresponds to an area of 0.5557 under the Normal Distribution.

3. The average age of statistics students nationwide is 22. The standard deviation is 2.5 years. Assume the age is a normally distributed variable. Find the probability that one student selected at random is older than 23.

4. You will create a statistics quiz of 15 questions by using a computer program that randomly generates questions. The program has a total of 60 questions stored. Any quizzes that have the same questions just in a different order are considered to be the same quiz. How many different arrangements of quizzes are possible? You may leave your answer in "probability notation."

5. You are an American spy in eastern Afghanistan. At 6 o'clock, you are to transmit a secret message to your contact by taping a sequence of 3 capital letters of the alphabet in your window (example: ABC). Each arrangement of letters will be viewed as a different message by your contact. No letter can be used more than once. How many different messages are possible? You may leave your answer in "probability notation."

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#### Solution Summary

The solution explains how to use z-score and z-table to find the probability related to normal distributed variable. It also explains how to use combination to find out the number of possible messages.

7 Elementary Statistics Problems - dice probability and normal distribution

Problems must be worked out so that the average first year college student can understand them.

1. If a gambler rolls two dice and gets a sum of 10. he wins $10, and if he gets a sum of three, he wins$20. The cost to play is $5. What is the expectation of this game?

2. A recent study found that the average life expectancy of a person living in Africa is 53 years with a standard deviation of 7.5 years. If a person in Africa is selected at random, what is the probability that the person will die before the age of 65?

3. At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years. If an employee is picked at random, what is the probability that the employee has worked at the store for over 10 years?

4. The average age of a vehicle registered in the United States is 8 years, or 96 months. If a random sample of 36 vehicles is selected, find the probability that the mean of their age is between 98 and 100 months? Assume the standard deviation for the population is 15.

5. What is the z value such that 50% of the total area lies to the right of the curve in a normal distribution?

6. A survey of 250 lobster fishermen found that they catch an average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?

7. The standard deviation of a distribution is 20. If a sample of 225 is selected, what is the standard error of the mean?

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