Question

In: Statistics and Probability

A population of values has a normal distribution with μ=238.6 and σ=54. You intend to draw...

A population of values has a normal distribution with μ=238.6 and σ=54. You intend to draw a random sample of size n=128
Find P₈₄, which is the mean separating the bottom 84% means from the top 16% means.

P₈₄ (for sample means) = ___________

Expert Solution

Given that,

mean = = 238.6

standard deviation = = 54

n = 128

= 238.6

= / n = 54 /128=4.77

Using standard normal table,

P(Z < z) = 84%

= P(Z < z) = 0.84

z =0.99 Using standard normal table,

Using z-score formula

= z * +

= 0.99*4.77+238.6

= 243.32

orchestra answered 2 years ago

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