Question

Given that x is a normal variable with mean μ = 49 and standard deviation σ = 6.2, 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 = = 49

standard deviation = = 6.2

a)  P(x ≤ 60)

P(x 60) = P[(x - ) / (60-49) /6.2 ]

= P(z 1.7742)

Using standard normal table,

Probability = 0.9620

(b)  P(x ≥ 50)

P(x 50) = 1 - P(x   50)

= 1 - P[(x - ) / (50-49) / 6.2]

= 1 -  P(z 0.1613)  

= 1 - 0.5641   

Probability = 0.4359

(c)  P(50 ≤ x ≤ 60)

P( 50 x 60) = P[( 50-49)/ 6.2 (x - ) / (60-49)/ 6.2]

P(50 x 60)  = P(0.1613 z 1.7742)

P(50 x 60) = P(z 1.7742) - P(z .1613)

P(50 x 60) = 0.9620 - 0.4359

Probability = 0.5261