Question

Marks on a public health test follow a normal distribution with a mean of 77 and a standard deviation of 11. What is the approximate 40th percentile of the mark distribution (40% of data is equal or less than what mark)?

Answer 1

58.

Explanation:

We have been given that marks on a public health test follow a normal distribution with a mean of 77 and a standard deviation of 11. We are asked to find the approximate 40th percentile of the mark distribution.

We will use z-score formula and normal distribution table to solve our given problem.

`z=(x-\mu)/(\sigma)`, where,

z = Z-score,

x = Sample score,

`\mu` = Mean,

`\sigma` = Standard deviation.

`z=(x-77)/(11)`

From normal distribution table, we need to find z-score corresponding to 40th percentile or 0.40.

`-1.75=(x-77)/(11)`

Let us solve for x.

`-1.75*11=(x-77)/(11)*11`

`-19.25=x-77`

`-19.25+77=x-77+77`

`57.75=x`

`x\approx 58`

Therefore, the approximate 40th percentile of the mark distribution would be 58.