MATH SOLVE

2 months ago

Q:
# A manufacturer produces a large number of toasters. From past experience, the manufacturer knows that approximately 1% are defective. In a quality control procedure, we randomly select 50 toasters for testing. We want to determine the probability that no more than one of these toasters is defective.

Accepted Solution

A:

Answer:The probability is 0.9106Step-by-step explanation:The variable that says the number of defective toasters follows a binomial distribution, where we have n identical and independent events (50 toasters) with a probability p of success (1% are defective) and a probability 1-p of fail (99% are not defective). So the probability that x toasters from the 50 are defective is:[tex]P(x) = \frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x} \\P(x) = \frac{50!}{x!(50-x)!}*0.01^{x}*(1-0.01)^{50-x}[/tex]Then, the probability P that no more than one of these toasters is defective is:P = P(0) + P(1)So, P(0) and P(1) are calculated as:[tex]P(0)=\frac{50!}{0!(50-0)!}*0.01^{0}*(1-0.01)^{50-0}=0.6050[/tex][tex]P(1)=\frac{50!}{1!(50-1)!}*0.01^{1}*(1-0.01)^{50-1}=0.3056[/tex]Finally, P is equal to:P = 0.6050 + 0.3056 = 0.9106