A population of values has a normal distribution with μ=81μ=81
and σ=39σ=39. You intend to draw a random sample of size
n=176n=176. State answers to one decimal places.
Find P92, which is the score separating the
bottom 92% scores from the top 8% scores.
P92 (for single values) =
Find P92, which is the mean separating the
bottom 92% means from the top 8% means.
P92 (for sample means) =
Solution :
Given that ,
mean = = 81
standard deviation = = 39
a ) P( Z < z) = 92%
P(Z < z) = 0.92
z = 1.41
Using z-score formula,
x = z * +
x = 1.41 * 39 + 81
= 135.99
P92 = 136.0
b ) n = 176
= 81
= / n = 39 / 176 = 2.9397
P( Z < z) = 92%
P(Z < z) = 0.92
z = 1.41
Using z-score formula,
= z * +
= 1.41 * 2.9397+ 81
= 85.14
P92 = 85.1
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