Central limit theorem: Sample proportion
The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is
no malfunction, the defect rate inthe manufacturing process (due to imperfections in the material used) is 1%. When 1.5% or more of the light bulbs in the
sample of 4400 are defective, the control unit calls repair technicians for service.
Answer the following. (If necessary, consult a list of formulas.)
(a) Find the mean of P, where p is the proportion of defective light bulbs in a sample of 4400 when there is no malfunction.
(b) Find the standard devition
(c) Compute an approximation for PCP >0.015), which is the probability that the service technicians will be called even though the system is functioning
properly. Round your answer to four decimal places.