A data set with a mean of 34 and a standard deviation of 2.5 is normally distributed.
According to the Empirical Rule, what percent of the data is in each of the following ranges? Round to the nearest tenth of a percent if necessary.

Between
34 and 39 Less than 31.5 Between
29 and 36.5
Percentage
%
%
%

a) From the mean and 2 deviations above we have 95/2% = 47.5% of the data

b) Below one deviation from the mean we have (50-34)% =16% of the data

c) One deviation below the mean and 2 deviations above we have (47.5%) +34% = 81.5% of the data

Step-by-step explanation:

For this case we know that for a random variable X we have:

The empirical rule states that within one deviation from the mean we have 68% of the values, within 2 deviations 95% and ithin 3 deviations 99.7% of the data.

So then we want to find the % between 34 and 39. We can use the z score formula given by:

In order to calculate the deviations from the mean and replacing we got:

And from the mean and 2 deviations above we have 95/2% = 47.5% of the data

For the probability that would be less than 31.5 we find the z score:

And below one deviation from the mean we have (50-34)% =16% of the data

And for the last part between 29 and 36.5 we find the z scores and we got:

And from one deviation below the mean and 2 deviations above we have (47.5%) +34% = 81.5% of the data

35x 3= 105

step-by-step explanation:

35+35= 70   70 + 35= 105