Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 120 and 171lb. The new population of pilots has normally distributed weights with a mean of 130 lb and a standard deviation of 33.4 lb. If a pilot is randomly selected, find the probability that his weight is between 120 lb and 171 lb.

Answer 1

Since the new population of pilots has normally distributed weights, we will calculate the Z-score in this problem.

Now, the weights follow normal distribution with a mean of 130 lb and a standard deviation of 33.4 lb. Let X denote the weights, then X follows normal with given mean and standard deviation.

Now we need the probability that a randomly selected pilot weights between 120 lb and 171 lb. Or, in other words, we need P(120<X<171).

Again, for X=120, Z= (X-mean)/SD= (120-130)/33.4 = -10/33.4= -0.2994011976

and , for X= 171, Z= (X- mean)/SD= (171-130)/33.4= 1.2275449102

Now, P(120<X<171)= P(-0.2994011976<Z<1.2275449102)= P(Z<1.2275449102)- P(Z<- 0.2994011976)

= 0.8907- {1- P(Z<0.2994011976)}

= 0.8907- (1- 0.6179)

= 0.8907- 0.3821

= 0.5086,

which is the required probability.