Question

Bob's exam score was $2.17$ standard deviations above the mean.

The exam was taken by $200$ students.

Assuming a normal distribution, how many scores were higher than bob's?

Answer 1

To find scores higher than Bob's:

Step-1: Find the probability that a score would be to the left of, or less than, $2.17$.

A $z-$score tells the number of standard deviations a data point is from the mean.

Since Bob's score is $2.17$ standard deviations above the mean, that means his $z-$score is $2.17$.

Using a $z-$table, we find the probability that a score would be to the left of, or less than, this value.

In the table, this is $0.9850$.

Step-2: Find the percentage of people that scored higher than Bob:

However, we are interested in the number of people that scored higher than Bob.

This means we subtract this from $1$ :

$1-0.9850=0.015$

This is the percentage of people that scored higher than Bob.

Step-3 : Convert $0.015$ into percentage.

To convert to a percent, multiply by $100$ :

$0.015\times 100=1.5$

To find the number of people that scored higher than Bob, take $1.5\%$ of $200$ :

$0.015\times 200=3$

Hence, $\mathbf{3}$ students scores were higher than Bob's.