Question

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

Answer 1

Answer:

a) z = 1.40

b) X is greater than or equal to 4.9

Step-by-step explanation:

Population mean (μ) = 1.54

Standard deviation (σ) = 2.40

The z-score for any given value X is:

$z=\frac{X-\mu}{\sigma}$

a) For X= 4.9:

$z=\frac{4.9 -1.54}{2.40}\\z= 1.40$

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.