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?

%

Question

Isabella Callahan

Mathematics

11 July, 22:11

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?

%

+2

Answers (1)

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Acosta · 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