Name: ______________________________________ Module 05 Homework Assignment 1.) Find the value of z of the standard normal random variable z for the following probabilities. Show calculations for each computation. a) P(z < z) = 0.95 b) P(2 < z < z) = .9710 2.) A randomly selected student is given a practice test. The test scores are normally distributed with a = 0 and = 1. Find the following probability of each z-score and show calculations for each computation. a.) P(z < 2.33) b.) P(z > 1.92) c.) P(-1.52 < z < 2.50) d.) P(z > -0.84) e.) P(1.34 < z < 3.26) 3.) Doctors believe that the heights of children in a specific age group are normally distributed with =63. and =2.5. . A child is randomly selected and their height is measured. Find each of the following probabilities and show calculations for each computation. a) Find the probability that the child's height is between 60 in. and 70 in. b) Find the probability that the child's height is greater than 67 in. c) Find the probability that the child's height is less than 60 in. 4.) The time a patient spends waiting in the emergency room is normally distributed with =6.1 hours and =1 hour. A patient is randomly selected and their weight time is measured. Find the wait times and show calculations for each computation. a) What wait time represents the 80th percentile? b) Between what to values does the middle 50 percent of wait times lie? c) What wait time represents the 95th percentile? 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: a.) If we know that the population's mean weight is 2.5g, what can we conclude about the mean of the sample means? b.) What can you conclude about the shape of the distribution of the sample means? 6.) A veterinarian is interested in studying the weights of poodles. She takes a random sample of n=68 poodles from a population with =19.6 and = 3.2. Based on this information, find the following probabilities. Be sure to interpret your results and show all steps for solving. a.) P ( x 19.6 ) b.) P ( x 19 ) c.) P ( x 20.1 ) d.) P (19.2 x 20.6 ) e.) P ( x 20.1 )