Question

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

and a standard deviation of 0 0485 What is the probability that a sample chosen at random has a proportion of registered
voters who vote between 0,37 and 0.39? Use the portion of the standard normal table below to help answer the question

Answer 1

The probability that a sample chosen at random has a proportion of registered voters who vote between 0.37 and 0.39, is 96.18%

Step-by-step explanation:

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 need to standardize the values using the z-score formula. The z-score is calculated as (x - mean) / standard deviation. In this case, the mean proportion of registered voters who vote is 0.38 and the standard deviation is 0.0485. So, for 0.37:

z = (0.37 - 0.38) / 0.0485 = -2.0619

Using the standard normal table, we can find the area to the left of -2.0619, which is approximately 0.0191. For 0.39:

z = (0.39 - 0.38) / 0.0485 = 2.0619

Again, using the standard normal table, we can find the area to the left of 2.0619, which is approximately 0.9809.

To find the probability between 0.37 and 0.39, we subtract the smaller area from the larger area: 0.9809 - 0.0191 = 0.9618, or 96.18%.

Answer 2

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.