A sample of concrete specimens of a certain type is selected

A sample of concrete specimens of a certain type is selected, and the compressive strength of each specimen is determined. The mean and standard deviation are calculated asx = 5000 and s = 400, and the sample histogram is found to be well approximated by a normal curve.
(a)Approximately what percentage of the sample observations are between 4600 and 5400? (Round the answer to the nearest whole number.)
Approximately   [Incorrect: Your answer is incorrect.] %

(b) Approximately what percentage of sample observations are outside the interval from 4200 to 5800? (Round the answer to the nearest whole number.)
Approximately  %

(c) What can be said about the approximate percentage of observations between 4200 and 4600? (Round the answer to the nearest whole number.)
Approximately  %

Solution

(a)P(4600<X<5400) = P((4600-5000)/400 <(X-mean)/s <(5400-5000)/400)

=P(-1<Z<1) =0.6827 (from standard normal table)

i.e. 68.27%

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(b) P(4200 <X< 5800)= P((4200-5000)/400 <Z<(5800-5000)/400)

=P(-2<Z<2) =0.9545 (from standard normal table)

i.e. 95.45%

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(c) P(4200 <X< 4600) = P((4200-5000)/400<Z<(4600-5000)/400)

=P(-2<Z<-1) =0.1359 (from standard normal table)

i.e. 13.59%