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A set of data has a normal distribution with a mean of 29 and a standard deviation of 4. Find the percent of data within each interval.

  1. from 25 to 33

A42%
B68%
C13%
D88%



  1. from 21 to 25

A28.5%
B54.5%
C13.5%
D15.5%


  1. greater than 29

A50%
B75%
C25%
D100%



  1. less than 21

A6.5%
B10.5%
C1.5%
D2.5%

Verified Answer :

nobillionaireNobley

Let x be the population distribution.
p(25 ≤ x ≤ 33) = p((25 - 29)/4 ≤ z ≤ (33 - 29)/4) = p(-1 ≤ z ≤ 1) = p(z ≤ 1) - p(z ≤ -1) = p(z ≤ 1) - [1 - p(z ≤ 1)] = 2p(z ≤ 1) - 1 = 2(0.84134) - 1 = 0.68268 = 68%

p(21 ≤ x ≤ 25) = p((21 - 29)/4 ≤ z ≤ (25 - 29)/4) = p(-2 ≤ z ≤ -1) = p(z ≤ -1) - p(z ≤ -2) = [1 - p(z ≤ 1)] - [1 - p(z ≤ 2)] = p(z ≤ 2) - p(z ≤ 1) = 0.97725 - 0.84134 = 0.13591 = 13.5%


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