Question

The quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to answer the following question. A quantitative data set of size 90 has mean 40 and standard deviation 6. Approximately how many observations lie between 22 and 58?

Approximately _____ observations lie between 22 and 58.

Answer 1

μ=40

σ=6

For x=22

z=(x-μ)/σ

=(22-40)/6

=-3

For x=58

z=(x-μ)/σ

=(58-40)/6

=3

P(22<x<58) = P(-3<z<3)

                  =0.997 {using emperical formula between 3 standard deviations from mean}

              

Hence,number of observations = n*p     

                                                  =90*.997

                                                  =90