Question

A population of values has a normal distribution with μ = 245.6 and σ = 59.3 . You intend to draw a random sample of size n = 21. Find P91, which is the mean separating the bottom 91% means from the top 9% means. P91 (for sample means) = 100.42

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 :

Given that,  

mean = = 245.6

standard deviation = = 59.3

= / n = 59.3 / 21 = 12.9403

Using standard normal table ,  

P(Z < z) = 91%

P(Z < 1.341) = 0.91

z = 1.341

Using z-score formula,  

= z * +   = 1.341 * 12.9403 + 245.6 = 263.0