Homework
Name: ______________________________________
Module 05 Homework Assignment
1.) Find the value of of the standard normal random variable for the following probabilities. Show calculations for each computation.
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a) P(z < zα) = 0.95 |
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b) P(2 < z < zα) = .9710 |
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2.) A randomly selected student is given a practice test. The test scores are normally distributed with a µ = 0 and σ = 1. Find the following probability of each z-score and show calculations for each computation.
a.) P(z < 2.33)
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b.) P(z > 1.92)
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c.) P(-1.52 < z < 2.50)
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d.) P(z > -0.84)
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e.) P(1.34 < z < 3.26)
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3.) Doctors believe that the heights of children in a specific age group are normally distributed with and. A child is randomly selected and their height is measured. Find each of the following probabilities and show calculations for each computation.
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a) Find the probability that the child’s height is between 60 in. and 70 in. |
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b) Find the probability that the child’s height is greater than 67 in.
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c) Find the probability that the child’s height is less than 60 in.
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4.) The time a patient spends waiting in the emergency room is normally distributed with hours and hour. A patient is randomly selected and their weight time is measured. Find the wait times and show calculations for each computation.
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a) What wait time represents the 80th percentile? |
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b) Between what to values does the middle 50 percent of wait times lie?
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c) What wait time represents the 95th percentile?
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5.) In one year a candy company manufactured 325 million pieces of candy. If we assume that on a given day of production, a sample of 75 pieces of candy are randomly selected and the mean weights are obtained, answer the following questions:
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a.) If we know that the population’s mean weight is 2.5g, what can we conclude about the mean of the sample means? |
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b.) What can you conclude about the shape of the distribution of the sample means?
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6.) A veterinarian is interested in studying the weights of poodles. She takes a random sample of poodles from a population with and 3.2. Based on this information, find the following probabilities. Be sure to interpret your results and show all steps for solving.
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a.) |
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b.) |
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c.) |
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d.) |
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e.) |
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