Standard Deviation and Normal Distribution Worksheet - Page 3

Standard Deviation and Normal Distribution Worksheet
• Page 3
21.
The average age of the employees in an organization is 34 years. Assume the variable is normally distributed and the standard deviation is 4. If 25 employees are selected at random, then find the probability that the sample mean age of the employees is less than 35 years.
 a. 89.44% b. 39.44% c. 10.56% d. 60.56%

Solution:

Since the variable is approximately normally distributed, the distribution of sample means will be approximately normal, with a mean of 34.

Let X be the sample mean age of the employees.

The standard deviation of the sample mean is σX = σn = 425 = 0.8

The problem is to find P(X < 35)

= P(X-μσ/n < 35 - 304/25) = P(z < 1.25)
[Convert X to standard normal units.]

= P(z < 0) + P(0 < z < 1.25) = 0.5000 + 0.3944 = 0.8944 = 89.34%
[Use the standard normal distribution table.]

The probability of sample mean age of the employees is less than 35 years is 89.44%.