Question 1: An aircraft manufacturing company is designing a new passenger seat. Currently three models have been produced. The company wishes to know which is the best model to adopt for the aircraft based on the following variables:
- safety
- comfort
- durability
- life-cycle cost
The company wishes to use "hard" data from tests and "soft" data from surveys.
Question 2: The seats were subjected to a safety stress test in which scores were assigned on a continuous scale of 0 to 10. This test was performed on a large sample of model C seats. The mean score was 6.8 with a standard deviation of 0.34. You may assume that the scores are normally distributed and the stated mean and standard deviation represent our best estimate of those population parameters.
A. Suppose model C seats were produced by the thousands and suppose we selected one at random from the huge warehouse full of them. What is the probability that we get a seat that would score above an 7.3 on the safety stress test?
B. What is the probability that you get a seat that would fail the stress test if failing is a score of 6.2 or less?
C. Estimate the probability that you get a seat that would score 7.2.(Note: A theoretical line has no width; consequently, a point estimate cannot be made using the area under the normal curve. This problem is circumvented by creating a strip and then estimating the area. For example 7.15<7.2<7.25. By finding the area bounded by x = 7.15 and x=7.25, we have an estimate for the probability of 7.2. Theoretically, this strip could be made as narrow as desired.)
D. Suppose you select a sample of 5 seats, subject each of them to the stress test and compute the mean score for the sample. What is the probability that the mean score will be less than 6.2?