Question

A Manufacturing Company has completed a study of its Cuddly Candy and found that their lifetimes are normally distributed with a mean of 40 years with a standard deviation of 7 years. Round answers to the nearest tenth of a year.

1. What is the minimum lifetime of Cuddly Candy that are in the top 11% of lifetimes?  
2. If the Company wants to offer a lifetime warranty on its candy, what is the maximum lifetime that the company should warranty so that no more than 5% of it candy will be eligible?  

Answer 1

Given that,

mean = = 40

standard deviation = =7

Using standard normal table,

P(Z > z) = 11%

= 1 - P(Z < z) = 0.11

= P(Z < z ) = 1 - 0.11

= P(Z < z ) = 0.89

= P(Z < 1.23 ) = 0.89  

z = 1.23 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x=1.23 *7+40

x= 48.96

x=49

(B)

Using standard normal table,

P(Z < z) = 5%

= P(Z < z) = 0.05

= P(Z < -1.64 ) = 0.05

z = -1.64 Using standard normal z table,

Using z-score formula  

x= z * +

x= -1.64*7+40

x= 28.52

x=29