Question

a random variable, X, is normally distributed with a mean of 100 and a standard deviation of 6.

What is the probability, Pr(X<100)? Answer Please use 4 significant digits

What is the probability, Pr(X>116)? Answer Please use 4 significant digits

What is the probability, Pr(90<X<110)? Answer Please use 4 significant digits

Answer 1

Solution :

P(x < 100) = P[(x - ) / < (100 - 100) / 6]

= P(z < 0)

= 0.5

Probability = 0.5

P(x > 116) = 1 - P(x < 116)

= 1 - P[(x - ) / < (116 - 100) / 6)

= 1 - P(z < 2.67)

= 1 - 0.9962

= 0.0038

Probability = 0.0038

P(90 < x < 110) = P[(90 - 100)/ 6) < (x - ) /  < (110 - 100) / 6) ]

= P(-1.67 < z < 1.67)

= P(z < 1.67) - P(z < -1.67)

= 0.9525 - 0.0475

= 0.9050

Probability = 0.9050