Question

A population of values has a normal distribution with μ = 247.3 and σ = 5.7. You intend to draw a random sample of size n = 12.

Find P72, which is the mean separating the bottom 72% means from the top 28% means. P72 (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

Given that,

mean = = 247.3

standard deviation = = 5.7

n = 12

= 247.3

= / n = 5.7 /12=1.6454

Using standard normal table,

P(Z < z) = 72%

= P(Z < z) = 0.72  

= P(Z <0.583 ) = 0.72

z = 0.583    Using standard normal table,

Using z-score formula  

= z * +   

=0.583 *1.6454+247.3

= 248.3