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 pilots weighing between 140 b and 181 has normally distributed weights with a mean of 149 lb and a standard deviation of 26.4 lb a?lf a pilot is randomly selected, find the probability that his weight is between 140 b and 181 lb. The new population of pilots The probability is approximately 0 5200 (Round to four decimal places as needed) b. If 40 different pilots are randomly selected. find the probability that their mean weight is between 140 lb and 181 lb. The probability is approximately (Round to four decimal places as needed)

Explanation / Answer

as z score=(X-mean)/std deviation

a)P(140<X<181)=P((140-149)/26.4<Z<(181-149)/26.4)=P(-0.34<Z<1.21)=0.8869-0.3669=0.5200

b)P(140<X<181)=P((140-149)/(26.4/sqrt(40))<Z<(181-149)/(26.4/sqrt(40)))=P(-2.16<Z<7.67)=1.00-0.0154=0.9846

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