Question

According to a Consumer Report, the mean replacement time of a television is 8.2 years with a standard deviation of 1.1 years. The distribution of TV replacement times is approximately Normal. Use a table or technology for each question. Include an appropriately labeled Normal curve for each part. There should be three separate curves.

1. What is the probability that a person will replace their TV after 12 years?

2. What is the probability that a person will replace their TV before 3 years?

3. What is the probability that a person will replace their TV between 6 and 10 years?

Answer 1

Solution :

Given that ,

mean = = 8.2

standard deviation = = 1.1

P(x >12 ) = 1 - P(x <12 )

= 1 - P[(x - ) / < (12 - 8.2) / 1.1]

= 1 - P(z <3.45 )

Using z table,

= 1 -0.9997

=0.0003

(B)

P(x <3 ) = P(( x -) / (3 - 8.2) /1.1 )

= P(z <-4.73 )

Using z table

= 0   

Using z table,  

P(6< x < 10) = P[(6 - 8.2) /1.1 < (x -) / < (10 - 8.2) /1.1 )]

= P( -2< Z <1.64 )

= P(Z <1.64 ) - P(Z < -2)

Using z table,  

=   0.9495 - 0.0228

= 0.9267