Question

A) The mean lifetime of a smartphone model is 3 years and 2 months with a standard deviation of 8 months. Assume normal distribution. What percentage of all smartphones should the manufacturer expect to replace if they offer a warranty period of 24 months?

B) What percentage of all smartphones should the manufacturer expect to replace, if they offer a warranty period of 28 months?

C) The CEO wants to budget for replacing not more than 8% of their smartphones during the warranty period. What is the maximum length of the warranty period that the company can offer? (Round down to the nearest month.)

Answer 1

Mean =   38 months = 3*12 + 2 months  
Sd = 8 months

a)
P( X<24) = ?
I know that, z = (X-mean)/(sd)  
z = (24-38)/8) = -1.7500

Hence,  
P( X<24) = P(Z<-1.75)
P( X<24) = NORMSDIST(-1.75)
P( X<24) = 4.01%

b)
P( X<28) = ?  
  
I know that, z = (X-mean)/(sd)  
z1 = (28-38)/8) = -1.2500
hence,  
P( X<28) = P(Z<-1.25)
P( X<28) = NORMSDIST(-1.25)
P( X<28) = 10.57%

c)
P(Z<z)   8%
z = NORMSINV(0.08)
z = -1.40507156
I know that, z = (X-mean)/sd  
(X-mean)/sd =   -1.4051
X = -1.4051*8+38
X = 26.76
X = 26 months