Question

A population of values has a normal distribution with
μ=144.2μ=144.2
and
σ=96.9σ=96.9.
You intend to draw a random sample of size
n=47n=47.

Find *
P*_{35},
which is the mean separating the bottom 35% means from the top 65%
means.

*
P*_{35}
(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.

Answer #1

Solution:

We are given that a random variable follows a normal distribution.

We are given

µ = 144.2

σ = 96.9

n = 47

We have to find 35^{th} percentile or P35 which is given
as below:

Z-critical value for bottom 35% area or top 65% area is given as below:

Z = -0.38532 (by using normal Z-table or excel)

Formula for finding percentile is given as below:

Percentile = X = µ + Z* σ

Percentile = 144.2 + (-0.38532)*96.9

Percentile = 144.2 - 0.38532*96.9

Percentile = 106.8625

Required Percentile = P_{35} = 106.9 (rounded to one
decimal place)

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1Info Details
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