Question

3. Under any normal distribution of scores, what percentage of the total area falls…

1. Between the mean and a score that is one standard deviation above the mean
2. Between the mean and two standard deviations below the mean
3. Within one standard deviation of the mean
4. Within two standard deviations of the mean

Answer 1

According to the Empirical rule, 68%, 95% and 99.7% falls within 1 , 2 and 3 standard deviations of mean respectively

a) Percentage of total area between the mean and a score that is one standard deviation above the mean = 68/2

= 34%

(Precise answer using standard normal distribution table is 34.13%)

b) Percentage of total area between the mean and two standard deviations below the mean = 95/2

= 47.5%

(Precise answer using standard normal distribution table is 47.72%)

c) Percentage of total area within one standard deviation of the mean = 68%

(Precise answer using standard normal distribution table is 68.27%)

d) Percentage of total area within two standard deviations of the mean = 95%

(Precise answer using standard normal distribution table is 95.45%)