Question

A large company claims that the average age of their employees is 32 years, with a standard deviation of 4 years. The average age of employees in the sales department at the company is 27 years. Given that the data is approximately normal, find the probability that an employee, chosen at random, will be younger than 27 years.

Answer 1

0.1056

Explanation:

A large company claims that the average age of their employees is 32 years i.e.
`\mu = 32`

Standard deviation =
`\sigma = 4`

The average age of employees in the sales department at the company is 27 years i.e.
`\bar{x}=27`

The z-score corresponding to x = 27 is calculated as:

`z=\frac{\bra{x}-\mu}{\sigma}`,

`z =(27-32)/(4) = -1.25`

Now, From a z-table,

The probability that x < 27 corresponds to the probability that z < -1.25:

P(z < -1.25) = 0.1056

Hence the probability that an employee, chosen at random, will be younger than 27 years is 0.1056

Answer 2

The z-score corresponding to x = 27 is calculated as:
z = (x - mu)/SD, where mu is the population mean of 32 years, and SD = 4 years. Then,
z = (27 - 32)/4 = -1.25
From a z-table, the probability that x < 27 corresponds to the probability that z < -1.25:P(z < -1.25) = 0.1056