The medical records of infants delivered at Kaiser Memorial

The medical records of infants delivered at Kaiser Memorial Hospital show that the infants\' lengths at birth (in inches) are normally distributed with a mean of 19 and a standard deviation of 2.4. Find the probability that an infant selected at random from among those delivered at the hospital measures the following. (Round your answers to four decimal places.)

(a) more than 20 in.

(b) less than 18 in.

(c) between 17 and 21 in.

Solution

Given that mean=19 and standard deviation sd=2.4
We need to find z-score using given formula
z = (x-mean)/sd

Ans a).
z=(20-19)/2.4=0.416666666667
which corresponds to a probability of 0.661539.
This is the probability that the speed is less than 20, so the probability that the speed is more than 20 is 1-0.661539 = 0.338461  

Ans b).
z=(18-19)/2.4=-0.416666666667
which corresponds to a probability of 0.338461

Ans c).
z=(21-19)/2.4=0.833333333333 which corresponds to a probability of 0.797672
z=(17-19)/2.4=-0.833333333333 which corresponds to a probability of 0.202328.
So required probability will be difference of both which is = 0.797672-0.202328= 0.595344