Problem 1: The amount of time it takes person to fall asleep at night after lying down is normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. a. What is the probability that it takes a random person more than 15 minutes to fall asleep? Even if you complete this problem using a calculator, you need to identify all information that you included in the calculator. [6 points] b. Draw the graph associated with Part A. You do not need to include all standard deviation lines. You only need to include the mean and value from the problem. [2 points] c. After talking to his doctor, Jack discovers that the normal amount of time it takes him to fall asleep is 1.5 standard deviations below the mean. How long does it normally take Jack to fall asleep after lying down? [4 points] d. If it takes Jenny 40 minutes to fall asleep, how many standard deviations away from the mean is her falling asleep time? Hint: Review the definition parts of your notes. What variable is in units of standard deviation? [3 points] e. Draw the graph associated with Part D. You do not need to include all standard deviation lines. You only need to include the mean and value from the problem. [2 points]
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