Question

Consider a normal distribution curve where the middle 35 % of the area under the curve...

Consider a normal distribution curve where the middle 35 % of the area under the curve lies above the interval ( 3 , 11 ). Use this information to find the mean, μ and the standard deviation, σ of the distribution.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Solution:

P(3<X<11) = 0.35

P(X<3) = (1 - 0.35)/2 = 0.325

Z = (X - mean)/SD

-0.45376 = (3 - mean)/SD

(by using z-table)

-0.45376*SD = (3 - mean)

Mean - 0.45376*SD = 3

(equation 1)

Now, we have

P(X>11) = (1 - 0.35)/2 = 0.325

Z = (X - mean)/SD

0.45376 = (11 - mean)/SD

0.45376*SD = (11 - mean)

Mean + 0.45376*SD = 11

(equation 2)

Now, solve equation 1 and 2 for the values of mean and SD.

By adding equation 1 and 2, we get

Mean - 0.45376*SD = 3

Mean + 0.45376*SD = 11

===========================

2*Mean = 14

Mean = 14/2 = 7

Mean = 7

Mean - 0.45376*SD = 3

7 - 0.45376*SD = 3

0.45376*SD = 7 - 3 = 4

SD = 4/0.45376 = 8.815233

SD = 8.815233

μ = 7

σ = 8.82

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