An insurance company finds that the ages of motorcyclists ki

An insurance company finds that the ages of motorcyclists killed in crashes are normally distributed with a mean of 26.9 years and a standard deviation of 8.4 years. If we randomly select on such motorcyclist, find the probability that he or she was under 25 years of age. If we randomly select 40 such motocyclists, find the probability that their mean age was under 25 years. Why do the probabilities in problems 4 and 5 differ? Explain in words using appropriate grammar, punctuation, and spelling.

Solution

a. z = ( x - ) /
P ( x < 25) = P ( z < -0.2262 ) = 0.4105

b. z = ( x - ) / (÷)
P ( x < 25) = P ( z < -1.4306 ) = 0.0763

the difference is because you are selecting more people and that affect the formula which means that affects the error of using the formula of normal distribution