Question

Given that x is a normal variable with mean μ = 42 and standard deviation σ = 6.1, 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

Solution :

Given that ,

mean = = 42

standard deviation = = 6.1

(a)

P(x 60) = P((x - ) / (60 - 42) / 6.1 = P(z 2.9508)

Using standard normal table,

P(x 60) = 0.9984

Probability = 0.9984

(b)

P(x 50) = 1 - P((x - ) / (50 - 42) / 6.1 = 1 - P(z 1.3115) = 1 - 0.9052

Using standard normal table,

P(x 50) = 0.0948

Probability = 0.0948

c)

P(50 x 60) = P((50 - 42/ 6.1) (x - ) / (60 - 42 / 6.1) )

P(50 x 60) = P(1.3115 z 2.9508)

P(50 x 60) = P(z 2.9508) - P(z 1.3115)

P(50 x 60) = 0.9984 - 0.9052 = 0.0932

Probability = 0.0932