Question

X is a normally distributed random variable with mean 72 and standard deviation 22. Use calculator to find the probability indicated.

P(78<X<127)

P(60<X<90)

P(X=80)

Answer 1

Solution :

Given that ,

mean = = 72

standard deviation = = 22

P(78 < x < 127) = P((78 - 72) / 22) < (x - ) /  < (127 - 72) / 22) )

= P(0.2727 < z < 2.5)

= P(z < 2.5) - P(z < 0.2727)

= 0.9938 - 0.6075

= 0.3863

P(78 < x < 127) = 0.3863

P(60 < x < 90) = P(60 - 72) / 22) < (x - ) /  < (90 - 72) / 22) )

= P(-0.5454 < z < 0.8181)

= P(z < 0.8181) - P(z < -0.5454)

= 0.7933 - 0.2927

= 0.5006

P(60 < x < 90) = 0.5006

P(X = 80) = 0