A survey found that people keep their television sets an ave

A survey found that people keep their television sets an average of 5.8 years with a standard deviation of 2.7 years and also that the data was approximately normally distributed. Calculate the probability that a person who has decided to buy a new television set has owned the old one.

A. more than 8.9 years

B. between 2.6 and 7.4 years

Solution

Normal Distribution
Mean ( u ) =5.8
Standard Deviation ( sd )=2.7
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 8.9) = (8.9-5.8)/2.7
= 3.1/2.7 = 1.1481
= P ( Z >1.148) From Standard Normal Table
= 0.1255                  
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 2.6) = (2.6-5.8)/2.7
= -3.2/2.7 = -1.1852
= P ( Z <-1.1852) From Standard Normal Table
= 0.11797
P(X < 7.4) = (7.4-5.8)/2.7
= 1.6/2.7 = 0.5926
= P ( Z <0.5926) From Standard Normal Table
= 0.72327
P(2.6 < X < 7.4) = 0.72327-0.11797 = 0.6053