Question

23.
Assume a data set is normally distributed with mean 172 and standard deviation 20. If the data set contains 400 data values, approximately how many of the data values will fall within the range 132 to 212?

Answer 1

anyone plss

Answer 2

Do you know the empirical rule for a Normal distribution?

Answer 3

The empirical rule states that approximately 95% of the data points lie in the range plus and minus 2 standard deviations of the mean.

Answer 4

I know the empirical rule. So this is how I solved it.
first I convert the 132 and 212 to a Z-score
z1=(132-172)\20=-2 and z2=(212-172)/20=2 then the empirical rule said it gives us a standard deviation of 95% so after I multiply .95*400 to get the data that will fall in the range or what will I do? Thanks for helping me :)

Answer 5

when I multiply .95 by 400= gave me 380 but the answer is 381.76 n it's said that the thing falls for 95.44% how did they got 95.44% I get confuse there

Answer 6

When I got -2 and 2 for z-score then I realize that they fall for 95% but then how did they got 95.44% or maybe I'm totally confuse

Answer 7

A more exact statement is:
The empirical rule states that approximately 95.44% of the data points lie in the range plus and minus 2 standard deviations of the mean.

Answer 8

ok thank you so much :)

Answer 9

You're welcome :)