Desperately need exact answer

Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 136 lb and a standard deviation of 33.9 lb. 

a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 171 lb.
The probability is approximately ? (need to round to four decimal places)

Answer 1

Obtain a z-score table

http://www.utdallas.edu/dept/abp/zscoretable.pdf

 

 

z = (X - μ) / σ

 

For 130 lb

z = (130 - 136) 33.9

z = -6 / 33.9

z = 0.1769

For this z the percent below is 4.75%

 

For 171 lb

z = (171 - 136) / 33.9

z = 35 / 33.9

z = 1.032

For this z the percent below is 84.85%

 

The percent between is 84.85% - 4.75% or 80.10%

 

Interpolation was not done for z-score of more than 2 decimal places.