Question

A normally distributed data set has a mean of 25 and a standard deviation of 2. Which percentage of the data falls between 23 and 25?

Answer 1

Approximately 34.13% of the data falls between 23 and 25 in a normally distributed data set with a mean of 25 and a standard deviation of 2.

Step-by-step explanation:

The percentage of data that falls between 23 and 25 in a normally distributed data set with a mean of 25 and a standard deviation of 2 can be found by calculating the area under the normal distribution curve between those two values.

First, we need to standardize the values using the formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For 23, Z = (23 - 25) / 2 = -1.

Next, for 25, Z = (25 - 25) / 2 = 0.

The area between these two Z values can be found using a standard normal distribution table or a calculator.

If we use a standard normal distribution table, we can find that the area to the left of Z = -1 is 0.1587 and the area to the left of Z = 0 is 0.5. To find the area between these two Z values, we subtract the area of Z = -1 from the area of Z = 0: 0.5 - 0.1587 = 0.3413. This means that approximately 34.13% of the data falls between 23 and 25 in the given normally distributed data set.

Answer 2

The answer is %34.13

Step-by-step explanation:

If mean of a normal distributed data set is 25, it will mean %50 of the data is above 25 and %50 of the data is below 25.

Than we need to subtract probability of being less than 23 from %50.

First z value need to be found for 23:

`z=(23-25)/2=-1`

probablity of z=-1 is %15.87

Then 50-15.87=34.13 %34.13 of the data falls between 23 and 25