Question

A population of values has a normal distribution with μ=81.3μ=81.3 and σ=88.7σ=88.7. You intend to draw a random sample of size n=168n=168.

Find P₈₀, which is the score separating the bottom 80% scores from the top 20% scores.
P₈₀ (for single values) =

Find P₈₀, which is the mean separating the bottom 80% means from the top 20% means.
P₈₀ (for sample means) =

Enter your answers as numbers accurate to 1 decimal place.
************NOTE************ round your answer to ONE digit after the decimal point! ***********
Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Given that,

mean = = 81.3

standard deviation = = 88.7

n = 168

= = 81.3

= / n = 88.7/ 168 = 6.84

Using standard normal table,

P(Z < z) = 80%

= P(Z < z) = 0.80  

= P(Z < 0.842) = 0.80

z = 0.842

Using z-score formula  

= z * +

= 0.842 * 6.84 + 81.3

= 87.1