The control department of a light bulb manufacturer randomly picks4400

light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is1

%

. When1.5

%

or more of the light bulbs in the sample of4400

are defective, the control unit calls repair technicians for service.Answer the following. (If necessary, consult alist of formulas.)

(a)Find the mean ofp

, wherep

is theproportion of defective light bulbs in a sample of4400

when there is no malfunction.

(b)Find the standard deviation ofp

.

(c)Compute an approximation forP

p

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.