Question

10% of all electrical batteries are defective. In a random selection of 50 of these batteries, find the probability that (a). There are no defective batteries. (b). More than 15% of the batteries are defective. (c). Between 8 and 12% of the batteries are defective.

Answer 1

(a)

Binomial Distribution

n = 50

p = 0.1

So,

q = 1 - p = 0.9

So,

Answer is:

0.0052

(b)

15% of 50 = 7.5

= np = 50 X 0.1 = 5

= =

To find P(X>7.5):

Z = (7.5 - 5)/2.1213 = 1.1785

Table of Area Under Standard Normal Curve gives area = 0.3810

So,

P(X>7.5) = 0.5 - 0.3810 = 0.1190

So,

Answer is:

0.1190

(c)

8% of 50 = 4

12% of 50 = 6

= np = 50 X 0.1 = 5

= =

To find P(4<X<6):

Case 1: For X from 4 to mid value::

Z = (4 - 5)/2.1213 = - 0.4714

Table of Area Under Standard Normal Curve gives area = 0.1808

Case 2: For X from mid value to 6:

Z = (6 - 5)/2.1213 = - 0.4714

Table of Area Under Standard Normal Curve gives area = 0.1808

So,

P(4<X<6) = 2 X 0.1808 = 0.3616

So,

Answer is:

0.3616