Answer:
a) 0.6517; b) 0.9115; c) No
Step-by-step explanation:
For part a, we will use the formula for a z score of an individual:
Using a z table, we see that the area under the curve to the left of this value is 0.3483. However, we want the probability greater than this, which is the area to the right of this value under the curve; this means we subtract from 1:
1-0.3483 = 0.6517
For part b, we will use the formula for a z score of the mean of a sample:
Using a z table, we see that the area under the curve to the left of this value is 0.0885. This means the area under the curve to the right of this value is
1-0.0885 = 0.9115
For part c,
The fact that the probability that any 12 men on the elevator will have a mean weight greater than 167, putting their total weight above 2004 pounds, is 91% means the elevator does not have the appropriate limit. There is a high chance the maximum will be exceeded.