Case Study Chapter 6 and 7

Question

FOR FULL CREDIT SHOW EQUATIONS USED AND WORK.
ELEVATOR CAPACITY: Suppose an elevator has a maximum capacity of 16 passengers with a total weight of 2500 lbs. The mean weight of females is less than the mean weight of males so we will only look at male weights for this example. Assume that male weights follow a normal distribution with a population mean of 182.9 lbs. and a population standard deviation of 40.8 lbs.

Draw the distribution of male weights. Mark the mean and three standard deviations above and below the mean.

Find the probability that 1 randomly selected male has a weight greater than 156.25 lbs. (2500/16 = 156.25). Shade the area of interest on the curve above then solve.

Samples of size 16 are taken from the male population.
What is the mean and standard deviation of the sample mean weight?

Can we assume the distribution of is normal? Why?

Draw the distribution for the sample mean, , of men’s weight for samples of size 16. Mark the mean, , and three standard deviations above and below the mean on the distribution.

Find the probability that a sample of 16 males have a mean weight greater than 156.25 lbs. Shade the area of interest on the curve in part ii then solve.

Which probability is more important for accessing the safety of the elevator, the one from part b or the one from part c iii. Based upon your calculations, do you think the elevator is safe enough for general use, explain.

Repeat the analysis using an elevator with a capacity of 16 and a weight limit of 3500 lbs. Start with part b. Keep in mind you are now concerned with the weight 3500/16 instead of 2500/16.