Question

Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14?

68% of the data points lie between 10 and 14.

68% of the data points lie between 8 and 12.

68% of the data points lie between 10 and 18.

68% of the data points lie between 10 and 16.

Answer 1

"For any normal distribution, approximately 68% of the distribution will lie within one standard deviation of the mean.
That means that, for this distribution, 68% of it will lie between 14-4=10 and 14+4=18."

Answer 2

Option (c) is correct.

68% of the data points lie between 10 and 18.

Explanation:

Given : a normal distribution with a standard deviation of 4 and a mean of 14

We have to choose the sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.

Since, given 68% data.

We know mean of data lies in middle.

And standard deviation is distribute equally about the mean that is 50% of values less than the mean and 50% greater than the mean.

So, 68% of data lies

mean - standard deviation = 14 - 4 = 10

mean + standard deviation = 14 + 4 = 18

So, 68% of the data points lie between 10 and 18.