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(1 point) Consider a normal distribution curve where the middle 45 % of the area under...

(1 point) Consider a normal distribution curve where the middle 45 % of the area under the curve lies above the interval ( 5 , 20 ). Use this information to find the mean, μμ , and the standard deviation, σσ , of the distribution

Math   Statistics-And-Probability   
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Answer #1

we know that middle 45% corresponds to z value of 0.5978 (using the standard normal distribution table, it is two sided z critical value)

we have to find the value of and

we can write

setting the z score value, we get

subtracting equation 2 from equation 1,

we get

here will cancel out and using a-(-a) = a+ a = 2a for the standard deviation term, we get

1.1956

dividing both sides by 1.1956, we get

Now, setting the value of standard deviation equation 2 to get the value of mean

we get

adding 7.50239 on both sides, we get

So, the required values are

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