Statistics Question

Question

Given that x is a normal variable with mean μ = 45 and standard deviation σ = 7.1, find the following probabilities. (Round your answers to four decimal places.)

(a)  P(x ≤ 60)

 

(b)  P(x ≥ 50)

 

(c)  P(50 ≤ x ≤ 60)

Answer 1

a.

z = (60-45)/7.1 = 2.11

Pr(z<=2.11) = 0.9827

b.

z = (50-45)/7.1 = .7042

Pr(z>= .7042) = 0.2406.

c.

z = (60-45)/7.1 = 2.11

Pr(z<=2.11) = 0.9827

z = (50-45)/7.1 = .7042

Pr(z<= .7042) = 0.7594.

In between: .9827-.7594 = .2233