A data set with a mean of 34 and a standard deviation of 2.5 is normally distributed. Use this information for items 1-3.

Question

1. According to the Empirical Rule, what percent of the data is between 34 and 39? Round to the nearest tenth of a percent.
2. What data value is greater than approximately 80% of the distribution?

A: -36.1

B: 34.5

C: 36.1

D: 40.0

3. Find the percent of all the values in a normal distribution for which z<=1.00, to the nearest tenth of a percent.

Answer 1

1. Within 2 standard dev. from the mean we have (34-2(2.5) , 34+2(2.5)) = (29, 39) there are about 95% data. Hence, from 34 to 39 i.e. (34, 39) there are about 95/2 = 47.5% data
2. P(X<k) = 0.8 => P(Z< k-34/2.5) = 0.8. From the standard normal distribution table/ calculator, (k-34)/2.5 = 0.842. Therefore, k = 34+ 2.5(0.842) = 36.1
3. P(Z<= 1) = 0.841 from standard normal distribution table/ calculator . Therefore answer is 84.1%