A population is normally distributed with mean 18.4 and standard deviation 1.9.

Question

A population is normally distributed with mean 18.4 and standard deviation 1.9.

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

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

(c) Draw a sketch of the bell curve.

one standard deviation      (smaller value) (larger value) two standard deviations      (smaller value) (larger value) three standard deviations      (smaller value) (larger value) 13,7 15,6 17,5 19,4 21,3 23,2 25,1

Explanation / Answer

= 18.4

= 1.9

a) intervals for one standard deviation = (18.4 - 1.9 , 18.4 + 1.9) = (16.5 , 20.3)

intervals for two standard deviation = (18.4 - 2*1.9 , 18.4 + 2*1.9) = (14.6 , 22.2)

intervals for third standard deviation = (18.4 - 3*1.9 , 18.4 + 3*1.9) = (12.7 , 24.1)

b) percent of the data lies in one standard deviation interval = P(-1 < Z < 1)

                                                                                               = P(Z < 1) - P(Z < -1)

                                                                                               = 0.8413 - 0.1587

                                                                                               = 0.6826

                                                                                               = 68.26%

percent of the data lies in two standard deviation interval = P(-2 < Z < 2)

                                                                                               = P(Z < 2) - P(Z < -2)

                                                                                               = 0.9772 - 0.0228

                                                                                               = 0.9544

                                                                                               = 95.44%

percent of the data lies in third standard deviation interval = P(-3 < Z < 3)

                                                                                               = P(Z < 3) - P(Z < -3)

                                                                                               = 0.9987 - 0.0013

                                                                                               = 0.9974

                                                                                               = 99.74%

c) The last graph is the corect one.

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