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A population of values has a normal distribution with μ=87.4μ=87.4 and σ=41σ=41. You intend to draw...

A population of values has a normal distribution with μ=87.4μ=87.4 and σ=41σ=41. You intend to draw a random sample of size n=106n=106.

Find P6, which is the mean separating the bottom 6% means from the top 94% means.
P6 (for sample means) =

Enter your answers as numbers accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

SOLUTION:

Given that,

mean = = 87.4

standard deviation = = 41

n=106

= 87.4

= / n = 41/106=3.98

Using standard normal table,

P(Z < z) = 6%

= P(Z < z) = 0.06  

z = 1.555

Using z-score formula  

= z * +

= 1.555*3.98+87.4

= 93.6

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