A set of data has a normal distribution with a mean of 51 an

A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. What percent of this data lies within the interval of 4.2 to 5.1? Express your answer as a percent rounded to the nearest whole number.

A) 34%

B) 48%

C) 24%

D) 28%

Solution

We know that if a data distribution is normal, then about 68 % of the data values are within one standard deviation of the mean. Thus, 68 % of the data lies within the interval 5.1-0.9 to 5.1+0.9 i.e. 4.2 to 6.0. Hence about ½(68 %) = 34 % data lies within the interval of 4.2 to 5.1. Option A is the correct answer .