Question

The age in United States has a normal distribution with a mean 46 years and standard deviation 13 years. The children are classified as those younger than 18 years and the middle age citizens are those in the age group 18-55. If a citizen is randomly chosen, what is the probability that he/she is middle age

Answer 1

0.74

Explanation:

The middle age citizens are those in the age group of 18-55.

We solve this question using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Mean 46 years

Standard deviation 13 years

For x = 18 years

z = 18 - 46/13

z = -2.15385

Probability value from Z-Table:

P(x = 18) = 0.015626

For x = 55 years

z = 55 - 46/13

= 0.69231

Probability value from Z-Table:

P(x = 55) = 0.75563

The probability that he/she is middle age is

P(x = 55) - P( x = 18)

= 0.75563 - 0.015626

= 0.740004

Approximately = 0.74