Q1. Suppose there is indeed a 2% failure rate among all syringes. If you check 2

Question

Q1. Suppose there is indeed a 2% failure rate among all syringes. If you check 20 syringes chosen at random from among all syringes, what is the chance that you find at least 1 faulty syringe? (You may assume that syringes are chosen with replacement from a population in which 2% of syringes are faulty.)

Q2. Continue to assume that there really is a 2% failure rate. Find the smallest number of syringes you can check so that you have at least a 50% chance of finding a faulty syringe.

Q3. A doctor purchased 5 syringes and found 4 of them to be faulty. Assuming that there is indeed a 2% failure rate, what was the probability of exactly 4 out of 5 syringes being faulty?

Q4. Assuming that there is indeed a 2% failure rate, assign order to a list of the numbers 1 through 7, ordered by the size of the quantities described below from smallest to largest. For example, order will start with 2 because list item 2 ("Zero") is the smallest quantity.

1. One half

2. Zero

3. The chance that zero out of 5 syringes are faulty.

4. The chance that at least 1 out of 5 syringes is faulty.

5. The chance that exactly 4 out of 5 syringes are faulty.

6. The chance that at least 4 out of 5 syringes are faulty.

7. The chance that all 5 out of 5 syringes are faulty.

Explanation / Answer

Solution:-

1) The chance that you find at least 1 faulty syringe is 0.3324.

p = 0.02

n = 20

x = 1

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x > 1) = 0.3324

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