In: Statistics and Probability

A population of values has a normal distribution with μ = 49.1 and σ = 29.4 . You intend to draw a random sample of size n = 35 . Find P4, which is the mean separating the bottom 4% means from the top 96% means. P4 (for sample means) =

Solution

Given that,

mean = = 49.1

standard deviation = = 29.4

n = 35

_{}
=
= 49.1

_{}
=
/
n = 29.4 /
35 = 4.97

Using standard normal table,

P(Z < z) = 4%

= P(Z < z) = 0.04

= P(Z < -1.751) = 0.04

z = -1.751

Using z-score formula

= z *
_{}+
_{}

= -1.751 * 4.97 + 49.1

= 40.4

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