# 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.