Answer:
A) 0.5564; B) 0.8962; C) Choice D. Part (a) because the seat performance for a single pilot is more important.
Step-by-step explanation:
<u>For part A</u>,
We will find the z score for each value and then subtract the probabilities for each to give us the area between them. We use the z score for an individual value:
Our first X is 130 and our second X is 191. Our mean, μ, is 136 and our standard deviation, σ, is 28.5:
Using a z table, we can see that the area under the curve to the left of z = -0.21 is 0.4168; the area under the curve to the left of z = 1.93 is 0.9732. This means the area between them is
0.9732-0.4168 = 0.5564.
<u>For part B</u>,
We will find the z score for each value again and subtract them; however, since we have a sample we will use the z score for the mean of a sample:
Our first X-bar is 130 and our second is 191; our mean is still 136; our standard deviation is still 28.5; and our sample size, n, is 36:
The area under the curve to the left of -1.26 is 0.1038; the area under the curve to the left of 11.58 is 1.00:
1.00-0.1038 = 0.8962
<u>For part C</u>,
We want the probability that each individual pilot will be safe in these seats, so the value in part A is more important.
