Question

Some data X that is normally distributed has a µ = 100 and σ = 12.

a. What the Z score associated with X = 130?   

b. What is P(X ≥ 100)?

c. What is P(X ≤ 85)?

d. What is the X score associated with Z = 1.5?   

Answer 1

Solution:

Given the normal distribution with

µ = 100 and σ = 12

a)

X = 130

Z score = (X - )/ = (130 - 100)/12 = 2.50

Z score = 2.50
b)

P(X ≥ 100)

= P[(X - )/ (100 - )/]

= P[Z (100 - 100)/12]

= P(Z 0.00)

= 1 - P(Z < 0.00)

= 1 - 0.5000

= 0.5000

P(X ≥ 100) = 0.5000

c)

P(X ≤ 85)

= P[(X - )/ ≤ (85 - )/]

= P[Z <  (85 - 100)/12]

= P[Z < -1.25]

= 0.1056   ( use z table)

P(X ≤ 85) = 0.1056

d)

Z = 1.5

Using Z score formula ,

X = + (Z * ) = 100 + (1.5 * 12) = 118

X = 118