Question

Suppose the ages of students in your university follows a right skewed distribution with mean of 24 years and a standard deviation of 5 years. If we randomly select a sample of 100 students from this university, what is the probability the average age of the sample is less than 25?

Answer 1

2.28%

Explanation:

To calculate the probability, we first determine the z-score:

z = (x-μ)/(σ/√n)--------------------------------------------- (1)

x= 25 years

μ = 24 years

σ = 5 years

Substituting into equation (1) we have :

z = (25-24)/ (5/(√100)

= 1 / 0.5

= 2

Looking up the z-score table we have the probability of an average age greater than 25 is 0.9772 or 97.72%.

The probability of less than an average score of 25 years is:

1 - 0.9772 = 0.0228

= 2.28%