Question

Assume the random variable X is normally distributed with a mean μ = 50 and standard deviation σ = 4.5. Find the P (x > 60) (three-decimal accuracy) Find the P (35 < x < 55) (three-decimal accuracy) Find x so that the area below x is .12. (one-decimal accuracy)

Answer 1

Solution :

Given that ,

mean = = 50

standard deviation = = 4.5

(a)

P(x > 60) = 1 - P(x < 60)

= 1 - P((x - ) / < (60 - 50) / 4.5)

= 1 - P(z < 2.22)

= 1 - 0.9868   

= 0.0132

P(x > 60) = 0.0132

Probability = 0.013

(b)

P(35 < x < 55) = P((35 - 50)/ 4.5) < (x - ) / < (55 - 50) / 4.5) )

= P(-3.33 < z < 1.11)

= P(z < 1.11) - P(z < -3.33)

= 0.8665 - 0.0004.

= 0.8661

Probability = 0.866

(c)

P(Z < z) = 0.12

P(Z < -1.175) = 0.12

z = -1.175

Using z-score formula,

x = z * +

x = -1.175 * 4.5 + 50 = 44.7

x = 44.7