Question

Suppose x is a normally distributed random variable with μ = 14 and σ =2. Find each of the following probabilities.

a. P (x ≥ 14.5) b. P (x ≤ 11) c. P (14.42 ≤ x ≤ 19.46) d. P (9.12 ≤ x ≤ 16.77)

Answer 1

a. P(x ≥14.5) = 1-P(x≤14.5)
=1-P(z≤(14.5-14)/2)
=1-P(z≤0.25)
=1-0.59871 (using normal table)
= 0.50129
I'll try to do the others next.

Answer 2

b. P(x≤11) = P(z≤(11-14)/2)
=P(z≤-1.5)
=1- 0.93319 (-ve so do 1 minus)
= 0.06671

Answer 3

c. Split into P(x ≥14.42) - P(x ≤19.46)
=P(z ≥ (14.42-14)/2) - P(z ≤ (19.46-1)/2)
=P(z ≥ 0.21) - P(z ≤ 2.73)
=0.58317 + 0.99683 -
=0.58

Answer 4

d. P(x ≥ 9.12) - P(x ≤ 16.77)
=P(z ≥ -2.44) - P(z ≤ 1.385)
=0.99266 + 0.91774 - 1
=0.07492

Answer 5

actually that last line should be 0.9104

Answer 6

Thank you. I have another one with different numbers. Sorry I didnt get a chance to solve the first one.