An engineer is going to redesign an ejection seat for an airplane. The seat was

Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for weights between 130 and 181 lbs. The new pilots have normally distributed weights with a man of 136 and a standard deviation of 26.5 If 30 different pilots are randomly selected, find the probability that their mean weight is between 130 and 181

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for weights between 130 and 181 lbs. The new pilots have normally distributed weights with a man of 136 and a standard deviation of 26.5 If 30 different pilots are randomly selected, find the probability that their mean weight is between 130 and 181

Explanation / Answer

Solution:

Given in the question

Mean =136

Standard deviation = 26.5

We need to calculate P(130<Xbar<181) =p(xbar<181)-p(xbar<130)

Z = (130-136)/26.5/sqrt(30) = -1.2399

Z = (181-136)/26.5/sqrt(30) = 9.299

So from z table we can find p- value correspond to Z value

P(130<xbar<181) = 0.9999- 0.1075= 0.8924

So there is 89.24% chances to find their mean weight is between 130 and 181.

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