Question

For a normal distribution with mean of 35 and standard deviation of 3, compute the following:

A. What percent of all observations will fall between 32 and 38 ?


%


B. What percent of all observations will fall between 32 and 35 ?


%


C. What percent of all observations will fall above 35 ?


%


D. What percent of all observations will fall below 38 ?


%

Answer 1

A. The empirical rule tells you that 68% of observations fall within one standard deviation of the mean for a normal distribution. [32, 38] = 35 ±3, so your interval is within one standard deviation of the mean.
68% of observations will fall between 32 and 38

B. The distribution is symmetrical about the mean, so half of the observations in part A will be below the mean.
34% of observations will fall between 32 and 35

C. The distribution is symmetrical about the mean, so half the observations fall above the mean.
50% of observations will fall above 35

D. The distribution is symmetrical about the mean, so half the observations will fall below the mean, 35. As in part B, 34% will fall between the mean and one standard deviation above the mean, 38. The sum of these percentages is 84%.
84% of observations will fall below 38