Question

Suppose a random variable x is best described by a normal distribution with μ=30 and σ=3.1 .

1. Find the z -score of x=30 (Round your answer to 2 decimal places) .
Such a z -score is z=
2. Find the x -score that corresponds to the z -score is z =1.39 (Enter your answer to 2 decimal places) .
Such an x-score is x=

Answer 1

The z-score of x=30 is 0 and the x-score that corresponds to z=1.39 is approximately 34.30.

Step-by-step explanation:

To find the z-score of x=30, we need to calculate how many standard deviations away from the mean this value is. The z-score formula is z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

Plug in the values: z = (30 - 30) / 3.1 = 0 / 3.1 = 0

The z-score for x=30 is 0.

To find the x-score that corresponds to z=1.39, we need to rearrange the formula and solve for x: x = μ + (z * σ)

Plug in the values: x = 30 + (1.39 * 3.1) = 30 + 4.299 = 34.299

The x-score that corresponds to z=1.39 is approximately 34.30.