Question

For the next employee, what is the probability that the number of days of vacation taken is less than 10 days? What is the probability that the number of days of vacation taken is more than 21 days? Discuss the solutions and an explanation. Respond to your peers’ posts and offer your feedback on this topic.

Answer 1

The answer is below

Explanation:

The number of vacation days taken by employees of a company is normally distributed with a mean of 14 days and a standard deviation of 3 days. For the next employee, what is the probability that the number of days of vacation taken is less than 10 days? More than 21 days?

Answer: Z score is used in statistics to determine by how many standard deviations the raw score is above or below the mean. It is given by the equation:

`z=(x-\mu)/(\sigma)\\ \\x=raw\ score,\mu=mean,\sigma=standard\ deviation`

Given that: μ = 14, σ = 3

a) For x < 10

`z=(x-\mu)/(\sigma)\\ \\z=(10-14)/(3)=-1.33`

From the normal distribution table, P(x < 10) = P(z < -1.33) = 0.0918

b) For x > 21

`z=(x-\mu)/(\sigma)\\ \\z=(21-14)/(3)=2.33`

From the normal distribution table, P(x > 21) = P(z > 2.33) = 1- P(z < 2.33) = 1 - 0.9901 = 0.0099