Need help not good in this course

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 help rounding to the correct four decimal places)

Answer 1

Here you would set down

(130 − 136) ÷ 33.9 equal to -0.1769911504

and

(171 − 136) ÷ 33.9 equal to 1.032448378.

Feeding -0.1769911504 into a calculator program

based on an infinite power series from calculus

gives a probability of -0.0702423296.

Feeding 1.032448378 into the calculator program

based on this infinite power series gives a

probability of 0.3490689407.

Then gain the probability sought as

0.3490689407 − -0.0702423296

equal to 0.4193112703.

The first 1 after 0.4193 in 0.4193112703 is

less than 5 so write the probability as

Pr(130 ≤ WEIGHT ≤ 171) = 0.4193.