Question

In a hypothetical study looking at the scores of 100 people in an entrance exam, it was determined that the average score was 95 with a standard deviation of 10. What proportion of individuals in this population have a score greater than 115

Answer 1

Answer: 0.0228

Explanation:

Given : In a hypothetical study looking at the scores of 100 people in an entrance exam, it was determined that the average score was 95 with a standard deviation of 10.

i.e.
`\mu=95\ \ \&\ \sigma=10`

Let x denotes the scores.

We assume that the scores are normally distributed.

Then, the proportion of individuals in this population have a score greater than 115 will be :-

`P(x>115)=1-P(x\leq115)\\\\=1-P((x-\mu)/(\sigma)<(115-95)/(10))\\\\=1-P(z\leq2)\ \ [\because\ z=(x-\mu)/(\sigma)]\\\\=1-0.9772\ \ [\text{By z-table}]\\\\=0.0228`

Hence , the proportion of individuals in this population have a score greater than 115 = 0.0228