Question

Assume that X has a normal distribution, and find the indicated probability. The mean is u=15.2 and the population standard deviation is 0.9. Find the probability that X is greater than 15.2

Answer 1

0.5

Explanation:

First, find the z score.

z = (x − μ) / σ

z = (15.2 − 15.2) / 0.9

z = 0

Use a calculator or z-score table to find the probability.

P(X > 15.2)

= P(Z > 0)

= 0.5

Answer 2

Answer: the probability that X is greater than 15.2 is 0.5

Explanation:

Assume that X has a normal distribution, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

µ = mean

σ = standard deviation

From the information given,

µ = 15.2

σ = 0.9

We want to find the probability that X is greater than 15.2. It is expressed as

P(x > 15.2) = 1 - P(x ≤ 15.2)

For x = 15.2

z = (15.2 - 15.2)/0.9 = 0

Looking at the normal distribution table, the probability corresponding to the z score is 0.5