Question

A population of values has a normal distribution with μ=25.1 and σ=3.6. You intend to draw a random sample of size n=213. Please answer the following questions, and show your answers to 1 decimal place.

Find the value separating the bottom 25% values from the top 75% values.


Find the sample mean separating the bottom 25% sample means from the top 75% sample means.

Answer 1

SOLUTION

Using standard normal table,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.67 ) = 0.25

z = -0.67

Using z-score formula,

x = z * +

x = -0.67 * 3.6+25.1

x = 22.688

X=22.7

(b)

n = 213

= / n = 3.6/213=0.2450

Using standard normal table,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.67 ) = 0.25

z = -0.67

Using z-score formula,

= z * +   

= -0.67 * 0.2450+25.1

= 24.93585

=24.9