Question

The scores on a driver's test are normally distributed with a mean of 100. Find the score that is 2.5 standard deviations above the mean, if the standard deviation is 10.
125
105
110
115

Answer 1

To find the score that is 2.5 standard deviations above the mean, we need to multiply the standard deviation by 2.5 and add it to the mean.

Z = (X - μ) / σ

Where:
X = Score we want to find
μ = Mean (given as 100)
σ = Standard deviation (given as 10)
Z = Number of standard deviations

Using the formula, we can rearrange it to find X:

X = Z * σ + μ

X = (2.5)(10) + 100
X = 25 + 100
X = 125

Therefore, the score that is 2.5 standard deviations above the mean (100) is 125.