Question

A population of values has a normal distribution with μ=52.6μ=52.6 and σ=8.6σ=8.6. You intend to draw a random sample of size n=115n=115.

Find P₉₈, which is the score separating the bottom 98% scores from the top 2% scores.
P₉₈ (for single values) =

Find P₉₈, which is the mean separating the bottom 98% means from the top 2% means.
P₉₈ (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 :

mean = = 52.6

standard deviation = = 8.6

Using standard normal table,

P(Z < z) = 98%

P(Z < 2.054) = 0.98

z = 2.054

Using z-score formula,

x = z * +

x = 2.054 * 8.6 + 52.6 = 70.3

P ₉₈ = 70.3

n = 115

= 52.6

= / n = 8.6 / 115 = 0.802

= z * + = 2.054 * 0.802 + 52.6 = 54.2

P ₉₈ = 54.2