Question

A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100. You scored a 625. Calculate your z-score to the nearest hundredth (i.e. 2 decimal places).

z=

Answer 1

Answer: The required z-score = 1.25

Explanation:

Let x be a random variable that denotes the scores in the exam.

The formula for z-score =
`\frac{X-\text{mean}}{\text{standard deviation}}`

As per given, we have

X= 625, mean=500, standard deviation = 100

Z-score =
`(625-500)/(100)`

i.e. Z-score =
`(125)/(100)`

i.e. Z-score =1.25

Hence, the required z-score = 1.25