Answer to Question #286854 in Statistics and Probability for Sanford Namakando

Question

A pottery produces royal souvenir mugs. It is known that 6% are defective. If 20 mugs

are selected at random. Find the probability that the sample contains less than 5

defective mugs.

Answer 1

X = defective item

p = probability that royal souvenir mugs will be defective

$p=0.06$

$q=1-p=1-0.06=0.94$

$n=20$

The probability that the sample contains less than 5 defective mugs is:

$P(X<5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)$

$P(X<5)=[20\raisebox{0.25em}{$C$}0(0.06)^{0}(0.94)^{20-0}]+[20\raisebox{0.25em}{$C$}1(0.06)^{1}(0.94)^{20-1}]+[20\raisebox{0.25em}{$C$}2(0.06)^{2}(0.94)^{20-2}]+[20\raisebox{0.25em}{$C$}3(0.06)^{3}(0.94)^{20-3}]+[20\raisebox{0.25em}{$C$}4(0.06)^{4}(0.94)^{20-4}]$

$P(X<5)=0.2901+0.3703+0.0449+0.0860+.0233=0.8146$