According to the childrens growth chart that doctors use as

According to the children’s growth chart, that doctors use as a reference, the height of two-year-old boys is approximately normally distributed with a mean of 34.5 inches and a standard deviation of 1.3 inches.

1. What is the probability that Sammy, a two-year-old boy, will be less than 3 feet tall? (12 inches = 1 foot)

2.What is the probability that a random sample of 25 two-year-old boys has a mean height less than 35 inches?

Solution

Normal Distribution
Mean ( u ) =34.5
Standard Deviation ( sd )=1.3
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 36) = (36-34.5)/1.3
= 1.5/1.3= 1.1538
= P ( Z <1.1538) From Standard Normal Table
= 0.8757                  

b)
P(X < 35) = (35-34.5)/1.3
= 0.5/1.3= 0.3846
= P ( Z <0.3846) From Standard Normal Table
= 0.6497