In a particular city the age of the roofs of homes are appro

In a particular city, the age of the roofs of homes are approximately uni-

formly distributed between 2 and 10 years. (Note this implies the mean is µ = 6 years and

the standard deviation is = 2:309 years). If a random sample of 64 homes is selected, what

is the probability that the sample mean roof age will be between 5.4 and 6.2 years?

Solution

Normal Distribution
Mean ( u ) =6
Standard Deviation ( sd )=2.309
Number ( n ) = 64
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 5.4) = (5.4-6)/2.309/ Sqrt ( 64 )
= -0.6/0.2886
= -2.0788
= P ( Z <-2.0788) From Standard Normal Table
= 0.01882
P(X < 6.2) = (6.2-6)/2.309/ Sqrt ( 64 )
= 0.2/0.2886 = 0.6929
= P ( Z <0.6929) From Standard Normal Table
= 0.75583
P(5.4 < X < 6.2) = 0.75583-0.01882 = 0.7361