Question

A population of values has a normal distribution with μ=99.5 and σ=83.2. You intend to draw a random sample of size n=197. Please answer the following questions, and show your answers to 1 decimal place.

Find P77, which is the value (X) separating the bottom 77% values from the top 23% values. P77 (for population) =

Find P77, which is the sample mean (¯x) separating the bottom 77% sample means from the top 23% sample means. P77 (for sample means) =

Answer 1

Solution :

Given that,  

mean = = 99.5

standard deviation = = 83.2

Using standard normal table ,

a.

P(Z < z) = 77%

P(Z < 0.74) = 0.77

z = 0.74

Using z-score formula,

x = z * +

x = 0.74 * 83.2 + 99.5 = 161.1

P77 = 161.1

b.

n = 197

= 99.5

= / n = 83.2 / 197 = 5.9278

P(Z < z) = 77%

P(Z < 0.74) = 0.77

z = 0.74

= z * + = 0.74 * 5.9278 + 99.5 = 103.9

P77 = 103.9