Question

A population of values has a normal distribution with μ=212.4μ=212.4 and σ=9.2σ=9.2. You intend to draw a random sample of size n=208n=208.

Find P₁₆, which is the score separating the bottom 16% scores from the top 84% scores.
P₁₆ (for single values) =

Find P₁₆, which is the mean separating the bottom 16% means from the top 84% means.
P₁₆ (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:-

Given that,

mean = = 212.4

standard deviation = = 9.2

Bottom 16%

n = 208

= = 212.4

= / n = 9.2 / 208 = 0.6379

P(Z < z ) = 0.16

z = -0.994

= z * + = (-0.994) *0.6379 + 212.4

= 211.77

Top 84%

P(Z > z ) = 0.84

1- P(z < z) =0.84

P(z < z) = 1- 0.84 = 0.16

z = -0.994

Using z-score formula,

= z * + = (-0.994) *0.6379 + 212.4

= 211.77

P16 = 211.77