Question

what percentile of the observations falls in two standard deviations from the mean?

Frequency Distribution;

1.5 to 4.5    3

4.5 to 7.5    5

7.5 to 10.5    9

10.5 to 13.5 5

13.5 to 16.5 3

Answer 1

From the given data

Histogram :

The shape of the histogram is perfect bell shaped so the given data is follows normal distribution

The percentile of the observations falls in two standard deviations from the mean is

P(Mean - 2SD < X < Mean + 2SD) = P(9-2*3.4986 < X < 9+2*3.4986) = P(2.0028< X < 15.9972) = 0.9545

since the data follows normal distribution