Question

A population of values has a normal distribution with μ=153 and σ=39.5 You intend to draw a random sample of size n=196

Find P₂, which is the score separating the bottom 2% scores from the top 98% scores.
P₂ (for single values) =

Find P₂, which is the mean separating the bottom 2% means from the top 98% means.
P₂ (for sample means) =

Enter your answers as numbers accurate to 1 decimal place. Answers obtained using z-scores rounded to 2 decimal places are accepted.

Answer 1

Solution :

Given that,

mean = = 153

standard deviation = = 39.5

n = 196

= 153

= / n = 39.5 / 196 = 2.8214

Using standard normal table,  

P(Z < z) = 2%

P(Z < -2.05) = 0.02

z = -2.05

Using z-score formula,

= z * + = -2.05 * 2.8214 + 153 = 147.2

P₂ = 147.2