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

Answer:

58.

Step-by-step 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.

$z=\frac{x-\mu}{\sigma}$, where,

z = Z-score,

x = Sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

$z=\frac{x-77}{11}$

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

$-1.75=\frac{x-77}{11}$

Let us solve for x.

$-1.75*11=\frac{x-77}{11}*11$

$-19.25=x-77$

$-19.25+77=x-77+77$

$57.75=x$

$x\approx 58$

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