Question

Scores on a test are normally distributed with a mean of 70 and standard deviation of 10. Applying the Empirical Rule, we would expect the middle 95% of scores to fall between what two values?

40 and 100

50 and 90

55 and 85

60 and 80

65 and 75

Answer 1

According to Empirical rule;

Approximately 95% data will fall into two standard deviation of the mean or in other way between mean and -2 times the standard deviation or mean and 2 times the standard deviation.

That is mathematical form :- μ ± 2σ

In above problem mean = 70 and standard deviation = 10

Hence the 95% data will fall in between

(70-2*10) and ( 70+ 2*10)

Or

(50,90)

Hence Answer will be 50 and 90