Question

A population is normally distributed with mean 19.2 and standard deviation 1.3.

(a) Find the intervals representing one, two, and three standard deviations of the mean.

one standard deviation:

two standard deviations:

three standard deviations:

(b) What percent of the data lies in each of the intervals in part (a)? (Round your answers to two decimal places.)

one standard deviation:

two standard deviations:

three standard deviations:

Answer 1

Answer:

Given,

Mean = 19.2

Standard deviation = 1.3

a)

One standard deviation = [u - , u + ]

= [19.2 - 1.3 , 19.2 + 1.3]

= [17.9 , 20.5]

Second standard deviation = [u - 2, u + 2]

= [19.2 - 2*1.3 , 19.2 + 2*1.3]

= [16.6 , 21.8]

Three standard deviation = [u - 3 , u + 3]

= [19.2 - 3*1.3 , 19.2 + 3*1.3]

= [15.3 , 23.1]

b)

Percentage of data lies each of intervals in part a are 69% , 95% , 99.8%.