Question

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual for a sample n=61 find the probability of a sample mean being less than 20.1 if mean=20 and standard deviation=1.3

Answer 1

The probability of the sample is 0.5 or 50%

Explanation:

Given:

Mean, μ = 20

Standard deviation, δ = 1.3

Probability of sample being less than 20.1 = ?

P (x < 20.1) = 20.1 - μ / δ √n

P (x < 20.1) = $\frac{20.1 - 20}{1.3\sqrt{61} }$

                  = 0.0098

P( x < 20.1) = P(z < 0.0098)

P (z < 0.0098) = 0.5

The value of P is found out using a z score table.

Therefore, probability of the sample is 0.5 or 50%