Question

Suppose x is a normally distributed random variable with muequals16 and sigmaequals2. Find each of the following probabilities. a.​ P(xgreater than or equals16.5​)   b.​ P(xless than or equals14.5​)   c.​ P(17less than or equalsxless than or equals21.2​)   d.​ P(11.16less than or equalsxless than or equals18.84​) LOADING... Click here to view a table of areas under the standardized normal curve.

Answer 1

P(X < A) = P(Z < (A - )/)

= 16

= 2

a) P(X 16.5) = 1 - P(X < 16.5)

= 1 - P(Z < (16.5 - 16)/2)

= 1 - P(Z < 0.25)

= 1 - 0.5987

= 0.4013

b) P(X 14.5) = P(Z < (14.5 - 16)/2)

= P(Z < 1.5)

= 0.9332

c) P(17 X 21.2) = P(X < 21.2) - P(X < 17)

= P(Z < (21.2 - 16)/2) - P(Z < (17 - 16)/2)

= P(Z < 2.6) - P(Z < 0.5)

= 0.9953 - 0.6915

= 0.3038

d) P(11.16 < X < 18.84) = P(X < 18.84) - P(X < 11.16)

= P(Z < (18.84 - 16)/2) - P(Z < (11.16 - 16)/2)

= P(Z < 1.42) - P(Z < -2.42)

= 0.9222 - 0.0078

= 0.9144