Question

A normal distribution has a mean of 85.7 and a standard deviation of 4.82. Find the data value corresponding to the value of z given. (Enter your answer to four decimal places.)

z = 2.65

Answer 1

To find the data value for a z-score of 2.65 with a mean of 85.7 and standard deviation of 4.82, use the formula x = μ + (z)(σ). The calculated data value is 98.4730 when rounded to four decimal places.

Step-by-step explanation:

To find the data value corresponding to a given z-score in a normal distribution, we use the formula:

x = μ + (z)(σ)

Given that the mean (μ) is 85.7, the standard deviation (σ) is 4.82, and the z-score (z) is 2.65, we calculate the data value (x) as follows:

x = 85.7 + (2.65)(4.82)

x = 85.7 + 12.773

Therefore, the data value corresponding to z = 2.65 is:

x = 98.473

Round the calculated value to four decimal places, the data value is 98.4730.