Question

A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. Find the percent of data between 4.2 and 5.1.
A)about 68%
B)about 34%
C)about 16%
D)about 13.5%

Answer 1

A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. Find the percent of data between 4.2 and 5.1.

Answer: The correct option is B) about 34%

Proof:

We have to find $P(4.2$

To find $P(4.2$, we need to use z score formula:

When x = 4.2, we have:

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

          $=\frac{4.2-5.1}{0.9}=\frac{-0.9}{0.9}=-1$

When x = 5.1, we have:

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

          $=\frac{5.1-5.1}{0.9}=0$

Therefore, we have to find $P(-1$

Using the standard normal table, we have:

$P(-1$= $P(z$

                               $=0.50-0.1587$

                               $=0.3413$ or 34.13%

                               = 34% approximately

Therefore, the percent of data between 4.2 and 5.1 is about 34%