Given a normal distribution with a mean 100 and a standard

Given a normal distribution with a mean = 100, and a standard deviation = 10, what is the probability that:

a. X>75?

b. X<70?

c. X<80 or X>110?

d. Between what two X values (symmetrically distributed around the mean)are 80% of the values?

Given a normal distribution with a mean = 100, and a standard deviation = 10, what is the probability that:

Z value for 75, z=(75-100)/10 =-2.5

P( x >75) = P( z >-2.5)

=0.9938

Z value for 70, z=(70-100)/10 =-3.0

P( x <70) = P( z < -3.0)

= 0.0013

Z value for 80, z=(80-100)/10 =-2.0

P( x <80) = P( z < -2.0)

= 0.0228

Z value for 110 z=(110-100)/10 =1

P( x >110) = P( z >1)

= 0.1587

P(X<80 or X>110) = P( z <-2) +P( z >1)

=0.0228+0.1587

=0.1815

d. Between what two X values (symmetrically distributed around the mean)are 80% of the values?

Z value for central 80% of values are (-1.282, 1.282)

Lower x value =100-1.282*10 = 87.18

upper x value =100+1.282*10 = 112.82