Question

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. a) If we randomly select one such motorcyclist, find the probability that he or s he was under 25 years of age.

Answer 1

0.41053

Explanation:

The z-score, also known as standard score / z-value / normal score. It is a quantity without dimensions which can be used to determine number of standard deviations by which a number is far from the mean value. Numbers over the mean have positive z-scores and below the mean have negative.

Here X is below the the mean so the z score is negative.

As we know

Z Score = (x - μ) / σ

Z Score = ( 25 - 26.9 ) / 8.4

Z score = -0.2262

Now We calculate P Value

P(X<25)=P ( z < -0.2262 )

P(X<25) =1 - P ( z < 0.2262)

P(X<25) =1 - 0.58947

P(x<25) = 0.41053

The probability that he or she was under 25 years of age is 0.41053.

Answer 2

0.41053

Explanation:

[TeX]z=\frac{x-\mu}{\sigma}[/TeX]

[TeX]z=\frac{25-26.9}{8.4}[/TeX]

z=-0.2262

P(X<25)=P(z<-0.2262)

=1-P(z<0.2262)

=1-0.58947

P(x<25) = 0.41053

The probability that a randomly selected person is under the age of 25 is 0.41053.