2 Calculate the following probabilities for x where x is nor

2. Calculate the following probabilities for x, where x is normally distributed with a mean of
300 and a standard deviation of 20:
a. P(x > 320).
b. P(x < 290).
c. P(x < 325).
d. P(260 < x < 340).

Solution

a)P(X>320)=1-P(X,320)

calculate the z score= X-mean/sd

z score=(320-300)/20 =1

from the z table ,P(z<1)=.8413

Now.1-P(z<1)=1-.8413 =.1587

b)P(x<290)

z score=(290-300)/20=-.5

from the z table,P(z<-.5)=.3085

c)P(x<325)=(325-320)/20=.25

p(z<.25)=.5987

d)P(260<x,340)

P(260-300)/20 <z<(340-300)/20)

p(-2<z<2)

p(z<2)-p(z<-2)

.9772-.0228

.9544