Question

A population of values has a normal distribution with μ = 141.1 and σ = 21.9 . You intend to draw a random sample of size n = 144 . Find P35, which is the score separating the bottom 35% scores from the top 65% scores. P35 (for single values) = Find P35, which is the mean separating the bottom 35% means from the top 65% means. P35 (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 = = 141.1

standard deviation = = 21.9

n = 144

= 141.1

= / n = 21.9 / 144 = 21.9 / 12 = 1.825

Using standard normal table,

P(Z < z) = 0.35

P(Z < -0.385) = 0.35

z = -0.385

Using z-score formula,

x = z * +

x = -0.385 * 21.9 + 141.1 = 132.7

P35 (for single values) = 132.7

= z * + = -0.385 * 1.825 + 141.1 = 140.4

P35 (for sample means) = 140.4