Question

According to statistics, the distribution of ages for licensed drivers has a mean of 44.5 years and a standard deviation of 17.1 years. Assume the distribution of ages is normally distributed. (Give your answers correct to one decimal place.)

(a) What percentage of the drivers are between the ages of 17 and 22.
_______%

(b) What percentage of the drivers are younger than 25 years of age.
_____%

(c) What percentage of the drivers are older than 21 years of age.
______ %

(d) What percentage of the drivers are between the ages of 45 and 65.
_______%

(e) What percentage of the drivers are older than 75 years of age.
_______%

Answer 1

Here we have given that

X: the age of licensed drivers

= population mean =44.5 years

= population standard deviation=17.1 Years

(A)   

Now we want to find the percentage of the drivers are between the ages 17 and 22

i.e

For that 1^st we want to find the Zscore

For X= 17

Zscore = == -1.61

and For X= 22

Zscore = == -1.32

i.e we get =

= 0.0934-0.0537 ( using z standard normal talble)

=0.0397

we get

= 0.0397 = 4 %

and

the percentage of the drivers are between the ages 17 and 22 is 4%

(B)

Now we want to find the percentage of the drivers are younger than 25 years of age

i.e

For that 1^st we want to find the Zscore

For X= 25

Zscore = == -1.14

we get

P(Z > -1.14) = 1 - P( Z < -1.14)

= 1- 0.1271 using z standard normal table

=0.8729

= 87 %

We get

the percentage of the drivers are younger than 25 years of age =87%

i.e = 0.8729

(C)

Now we want to find the percentage of the drivers are Older than 21 years of age

i.e

For that 1^st we want to find the Zscore

For X= 21

Zscore = == -1.37

we get

P(Z > -1.37) = 1 - P( Z < -1.37)

= 1- 0.0853 using z standard normal table

=0.9147

=91 %

We get

the percentage of the drivers are older than 21 years of age =91%

(D)

Now we want to find the percentage of the drivers are between the ages 45 and 65

i.e

For that 1^st we want to find the Zscore

For X= 45

Zscore = == 0.03

and For X= 65

Zscore = == 1.20

i.e we get =

= 0.8849 - 0.5120 ( using z standard normal talble)

=0.3729

=37%

we get

= 0.3729 = 37 %

and

the percentage of the drivers are between the ages 45 and 65 is 37%

(E)

Now we want to find the percentage of the drivers are Older than 75 years of age

i.e

For that 1^st we want to find the Zscore

For X= 75

Zscore = == 1.78

we get

P(Z >1.78) = 1 - P( Z < 1.78)

= 1- 0.9625 using z standard normal table

=0.0375

=4 %

We get

the percentage of the drivers are older than 75 years of age =4%