Question

Let X be a normal random variable with a mean of 1.54 and a standard deviation of 2.40.

a)Calculate the corresponding z-score (z) for the point x = 4.9. Give your answer to 2 decimal places. z = 1.4
b)The area under the standard normal probability density function from z to infinity is interpreted as the probability that X is: less than or equal to 4.9 equal to 4.9 greater than or equal to 4.9

Answer 1

a) z = 1.40

b) X is greater than or equal to 4.9

Explanation:

Population mean (μ) = 1.54

Standard deviation (σ) = 2.40

The z-score for any given value X is:

`z=(X-\mu)/(\sigma)`

a) For X= 4.9:

`z=(4.9 -1.54)/(2.40)\\z= 1.40`

The corresponding z-score for x = 4.9 is z=1.40

b) Z-scores higher than 1.40 correspond to values of X higher than 4.9. Therefore, the area under the standard normal probability density function from z to infinity, P(z ≥ 1.40), is interpreted as the probability that X is greater than or equal to 4.9.