Question

Data are drawn from a relatively symmetric and bell-shaped distribution with a mean of 75 and a standard deviation of 5.

a.	What percentage of the observations fall between 65 and 85? (Round your answer to the nearest whole percent. )

Percentage of observations

b.	What percentage of the observations fall between 60 and 90? (Round your answer to the nearest whole percent. )

Percentage of observations

c.	What percentage of the observations are less than 65? (Round your answer to 1 decimal place.)

Percentage of observations

Answer 1

When the data is normally distributed, the empirical rule states that 68%, 95% and 99.7% of data values fall within 1, 2 and 3 standard deviations of mean respectively.

Mean = 75

Standard deviation = 5

a) 75 - 2x5 = 65

75 + 2x5 = 85

65 to 85 is the range of 2 standard deviations from mean

Percentage of observations between 65 and 85 = 95%

b) 75 - 3x5 = 60

75 + 3x5 = 90

60 to 90 is the range of 3 standard deviations from mean

Percentage of observations between 65 and 85 = 99.7%

c) 50% of observations are below 75

95/2 = 47.5% of observations are between 65 and 75

Percentage of the observations less than 65 = 50 - 47.5 = 2.5%