Question

What is the standard deviation of a normal distribution, whose mean is 35, in

which an value of 23 has a z-score of -1.63?
OA. 4.83
OB. 23.33
OC. 7.36
OD. 54.17
OE. 9.11

Answer 1

To find the standard deviation of a normal distribution, we can use the formula for z-score:

z = (x - μ) / σ

where z is the z-score, x is the value, μ is the mean, and σ is the standard deviation.

Given that the z-score is -1.63 for a value of 23, we can rearrange the formula to solve for the standard deviation σ:

σ = (x - μ) / z

Plugging in the values, we have:

σ = (23 - 35) / -1.63

σ ≈ 7.36 (rounded to two decimal places)

Therefore, the correct answer is OC. 7.36.