Question

A population of values has a normal distribution with μ=88.1 and σ=58.8. You intend to draw a random sample of size n=189.

Find P₇₁, which is the score separating the bottom 71% scores from the top 29% scores.
P₇₁ (for single values) =

Find P₇₁, which is the mean separating the bottom 71% means from the top 29% means.
P₇₁ (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

Solution :

Given that,  

mean = = 88.1

standard deviation = = 58.8

Using standard normal table ,

P(Z < z) = 71%

P(Z < 0.553) = 0.71

z = 0.553

Using z-score formula,

x = z * +

x = 0.553 * 58.8 + 88.1 = 120.6

P71 = 120.6

= / n = 58.8 / 189 = 4.2771

Using standard normal table ,  

P(Z < z) = 71%

P(Z < 0.553) = 0.71

z = 0.553

Using z-score formula,  

= z * +   = 0.553 * 4.2771 + 88.1 = 90.5

P71 = 90.5