Ch. 6 03/28/2020 Homework #6 Math 227 1.) Draw a density curve and use the table to determine the following. Let Z be a standard normal random variable, i.e. Z ~ N(=0, =1). a. P(Z > 1.23) Name: Show all relevant work for full credit. b. P(Z -1.645) c. P(Z-2.51) d. P(Z 0.91) 10.) Draw a density curve and use the calculator to determine the probability. Write the calculator function. The average GPA at a particular school is 2.89 with a standard deviation 0.63. If a random sample of 55 students is collected, find the probability that the average GPA for this sample is greater than 3.0. 11.) Draw a density curve and use the table to determine the following. The elevator in the car rental building at San Francisco International Airport has a placard stating that the maximum capacity is "4000 lb-16 passengers." Because 400016 = 250, this converts to a mean passenger weight of 250 lb when the elevator is full. We will assume a worst-case scenario in which the elevator is filled with 16 adult males. Assume that adult males have weights that are normally distributed with a mean of 230 lb and a standard deviation of 39 lb. Find the probability that a sample of 16 randomly selected adult males has a mean weight less than 250lb. 3.) Draw a density curve and use the table to determine the value of a. Let Z be a standard normal random variable, i.e. Z ~ N(=0, =1). a. P33 b. P(Za) = 0.0122 c. P(Za) = 0.85 d. P(Za) = 0.72 4.) Draw a density curve and use the calculator to determine the value of a. Write the calculator function. Let Z be a standard normal random variable, i.e. Z ~ N(=0, =1). a. D7 b. P(Za) = 0.94 c. P(Za) = 0.42 d. P(Za) = 0.125 7.) Draw a density curve and use the table to determine the following. The monthly incomes of trainees at a local office are normally distributed with a mean of $1,100 and a standard deviation $105. What percentage of trainees earn more than $950 a month? 8.) Draw a density curve and use the table to determine the following. Scores on the Midterm exam are normally distributed with mean of 60.5 and a standard deviation of 6. Find the score that separates the top 59% from the bottom 41%.