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
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.