Question

Q 29 A company makes ballpoint pens. The
probability that a ballpoint pen is
defective is 0.02. What is the probability
that a sample of 400 ballpoint pens will
contain exactly 5 defective ballpoint
pens?​

Answer 1

GIven:  The  probability that a ballpoint pen is  defective is 0.02

To find : What is the probability  that a sample of 400 ballpoint pens will

contain exactly 5 defective ballpoint  pens?​

Solution:

probability that a ballpoint pen is  defective is 0.02  ,  p = 0.02

probability that a ballpoint pen is  not defective q = 1  - p   = 1  - 0.02  = 0.98

p = 0.02

q = 0.98

P(x)  = ⁿCₓpˣqⁿ⁻ˣ

n = 400   ( samples)

x = 5      5 defective ball points

Probability  that a sample of 400 ballpoint pens will  contain exactly 5 defective ballpoint  pens

P(5)  =   ⁴⁰⁰C₅(0.02)⁵(0.98)³⁹⁵

= 0.091

0.091   is the probability  that a sample of 400 ballpoint pens will  contain exactly 5 defective ballpoint  pens

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