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

Answer:

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

Answer 2

The probability that the data falls between 23 and 25 is 34.13%

z score is used to determine by how many standard deviations the raw score is above or below the mean.

The z score is given by:

$z=\frac{x-\mu}{\sigma/ } \\\\where\ x\ is\ raw\ score,\mu\ is\ mean, \sigma\ is\ standard\ deviation$

Given that μ = 25, σ = 2 Hence for x > 23:

$z=\frac{23-25}{2} =-1$

x < 25:

$z=\frac{25-25}{2} =0$

From the normal distribution table:

P(23 < x < 25) = P(-1 < z < 0) = P(z < 0) - P(z < -1) = 0.5 - 0.1587 = 0.3413 = 34.13%

The probability that the data falls between 23 and 25 is 34.13%

Find out more on z score at: https://brainly.com/question/25638875