Question

if a pilot is randomly selected, find the probability that his weight is between 120 lb and 161 lb witha mean of 130 and 27.3

Answer 1

The probability that the weight of a randomly selected pilot is between 120 lbs. and 161 lbs. is 0.52.

Explanation:

Let X = weight of pilots.

It is provided that X follows a normal distribution with mean, μ = 130 lbs. and standard deviation, σ = 27.3 lbs.

Compute the probability that the weight of a randomly selected pilot is between 120 lbs. and 161 lbs. as follows:

`P(120<X<161)=P((120-130)/(27.3)<(X-\mu)/(\sigma)<(161-130)/(27.3))\\\\=P(-0.37<Z<1.14)\\\\=P(Z<1.14)-P(Z<-0.37)\\\\=0.87286-0.35569\\\\=0.51717\\\\\approx 0.52`

Thus, the probability that the weight of a randomly selected pilot is between 120 lbs. and 161 lbs. is 0.52.