Answer:
A. 0.62%
B. 28 months
Step-by-step explanation:
A. Calculation for what percentage of total production will the company expect to replace
Let x represents the distribution of life times
Let mean be 34 months
Let standard deviation be 4 months.
Based on the information the full refund on any defective watch for 2 years will represent 24 months (2 years *12 months).
First step
P(X<24)
= p(x-mean/ standard deviation< 24-34/4)
= p(z< -10/4)
=P(z<-2.5)
Second step is to Use the excel function to find NORMSDIST(z) of P(z<-2.5)
NORMSDIST(z)=0.62%
Therefore the percentage of total production will the company expect to replace will be 0.62%
B. Calculation for how much the guarantee period should be
First step
P(X<x)=0.06
P(x-Mean/Standard deviation < x-34/4) = 0.06
Second Step is to Use excel function
P(z<x-34/4) = (Normsinv(0.06)
x-34/4 = -1.555
Now let calculate how much the guarantee period should be
x = -6.22+34 months
x = 27.78
x = 28 months (Approximately)
Therefore the guarantee period should be 28 months
