If the fraction of defective covers produced on the USB Mouse Factory production line is known to be 8%, what is the probability that a sample of 10 covers will contain exactly 2 defectives?

14.78% probability that a sample of 10 covers will contain exactly 2 defectives

Step-by-step explanation:

For each cover, there are only two possible outcomes. Either it is defective, or it not. The probability of a cover being defective is independent from other covers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

If the fraction of defective covers produced on the USB Mouse Factory production line is known to be 8%, what is the probability that a sample of 10 covers will contain exactly 2 defectives?

This is when . So

14.78% probability that a sample of 10 covers will contain exactly 2 defectives

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.

333.74 ! should be your answer for this question