Question

1. A manufacturer of metal pistons claims that on average, only 5% of their pistons are bad (either oversize or undersize). When the pistons are delivered to a local store, a quality control staff will randomly select 10 pistons, and measure out if they are oversize or undersize. If he sees 3 or more pistons are bad, they will reject the delivery.

                                                                                                                                                         

1. If we assume that the fault rate for the manufacturer is as claimed 5%, what is the distribution of X, where X = number of bad pistons from the 10 randomly selected pistons?(Give the distribution name or symbol and corresponding parameters)

                                                                                                                           

                                                                                        

2. What is the sample space of the variable X above?

3. What is population mean and population standard deviation of variable X?

Answer 1

Solution:

1. If we assume that the fault rate for the manufacturer is as claimed 5%, what is the distribution of X, where X = number of bad pistons from the 10 randomly selected pistons?

X follows binomial distribution with n=10 and p=0.05

X~B(10,0.05)

2. What is the sample space of the variable X above?

X={0,1,2,3,4,5,6,7,8,9,10}

3. What is population mean and population standard deviation of variable X?

population mean=np=10*0.05=5

population standard deviation=sqrt(npq)

=sqrt(10*0.05*(1-0.05))

=sqrt(10*0.05*0.95)

= 0.6892024