Question

The mean score of a competency test is 82, with a standard deviation of 2. Between what two values do about 99.7% of the values lie?

Answer 1

99.7% lies between 76 and 88

Explanation:

mean = 82, standard deviation = 2

3 standard deviation has 99.7%

so we need to find 3 standard deviation above and below the mean.

To find 3 standard deviation above the mean , we add standard deviation 2 with mean

82 + 2= 84 first SD

84 + 2= 86 second SD

86 + 2= 88 third SD

88 is the third SD above the mean 82

To find 3 standard deviation below the mean , we subtract standard deviation 2 from mean

82 - 2= 80 first SD

80 - 2= 78 second SD

78 - 2= 76 third SD

76 is the third SD below the mean 82

So , 99.7% lies between 76 and 88

Answer 2

99.7% encompasses about 3 standard deviations either side of the mean.

82 ±3*2 = (76, 88)

About 99.7% of the values lie between 76 and 88.