Question

Assume that a normal distribution of data has a mean of 14 and a standard deviation of 2. Use the 68minus 95minus99.7 rule to find the percentage of values that lie above 12 .

Answer 1

Given that, mean = 14 and

standard deviation = 2

According to 68-95-99.7 (Empirical ) rule

i) about 68% of the data fall within 1 standard deviations of the mean.

ii) about 95% of the data fall within 2 standard deviations of the mean.

iii) about 99.7% of the data fall within 3 standard deviations of the mean.

Here,

By rule i) 68% of the data fall within 1 standard deviations of the mean and remaining 100 - 68 = 32% of the data fall outside the interval from which 32/2 = 16% of the data fall below 1 standard deviations of the mean and 16% of the data fall above 1 standard deviations of the mean.

Therefore, the percentage of values that lie above 12 is,

68% + 16% = 84%

Answer: 84%