Question

The proportions of multiple samples of registered voters who vote are normally distributed with a mean proportion of 0.38

Answer 1

Answer: 0.1632

Step-by-step explanation:

Given : The proportions of multiple samples of registered voters who vote are normally distributed .

Mean proportion : $\mu=0.38$

Standard deviation : $\sigma: 0.0485$

Let x be the random variable that represents the proportion of registered

voters.

To find : The probability that a sample chosen at random has a proportion of registered  voters who vote between 0.37 and 0.39.

We first find z-score corresponds 0.37 and 0.39.

Formula for z-score : $z=\dfrac{x-\mu}{\sigma}$

For x= 0.37

$z=\dfrac{0.37-0.38}{0.0485}\approx-0.206$

For x= 0.39

$z=\dfrac{0.39-0.38}{0.0485}\approx0.206$

By using the standard normal table, the required probability will be :_

$P(0.37$

Hence, the probability that a sample chosen at random has a proportion of registered  voters who vote between 0.37 and 0.39 = 0.1632

Answer 2

Answer:

0.16

Step-by-step explanation:

I think you meant a standard deviation of 0.0485 and a range of 0.37 to 0.38.

Using a calculator with basic probability and statistic functions results in:

normcdf(0.37,0.39,0.38,0.0485) = 0.16.  This is the desired probability.