If 4 items are chosen at random, what is the probability that at least one will have a defect?

Nann
2021-09-15
Answered

A manufacturing machine has a 3% defect rate.

If 4 items are chosen at random, what is the probability that at least one will have a defect?

If 4 items are chosen at random, what is the probability that at least one will have a defect?

You can still ask an expert for help

sweererlirumeX

Answered 2021-09-16
Author has **91** answers

Step 1

Here, X denotes that the item is defective, which follows binomial distribution with$n=4ZKS{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}PSKp=0.03$ .

The formula to find the binomial probability is,

$P(X=x){=}^{n}{C}_{x}{p}^{x}{(1-p)}^{(n-x)}$

Step 2

Probability that at least one will have a defect:

The probability that at least one will have a defect is,

$P(X\ge 1)=1-P(X=0)$

$=1{-}^{4}{C}_{0}{\left(0.03\right)}^{0}{(1-0.03)}^{(4-0)}$

$=1-0.8853$

$=0.1147$

The probability that at least one will have a defect is 0.1147.

Here, X denotes that the item is defective, which follows binomial distribution with

The formula to find the binomial probability is,

Step 2

Probability that at least one will have a defect:

The probability that at least one will have a defect is,

The probability that at least one will have a defect is 0.1147.

asked 2021-05-21

At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of 40 freshmen sharing a common lounge area. How many international students would you expect to find in a typical cluster? With what standard deviation?

asked 2021-10-01

Eighty percent of households say they would feel secure if they had 50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. Find the probability that the number that say they would feel secure is exactly five, (b) more than five, and (c) at most five

c.) Find the probability that the number that say they would feel secure is at most five.

(round to three decimal places as needed).

asked 2021-09-25

A sample of 5 parts is drawn without replacement from a total population of 13 parts. Determine the probability of getting exactly 3 defective parts. The population is known to have 6 defective parts.

asked 2021-09-07

Assume a binomial probability distribution has p = 0.80 and n = 400.

a) what is the mean and standard deviation

b) is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.

c) what is the probability of 300 to 310 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

a) what is the mean and standard deviation

b) is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.

c) what is the probability of 300 to 310 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

asked 2021-02-19

The probability that a patient recovers from a stomach disease is 0.8. Suppose 20 people are known to have contracted this disease. What is the probability that exactly 14 recover?

asked 2021-02-05

1) State the formula for the Binomial Probability Distribution, also state the domain.
2) Tell what the requirement for the Binomial experiment are.
3) List both formulas for calculating the mean of a Binomial Probability Distribution.
4) List the formulas for the standard deviation of a Binomial Probability Distribution.

asked 2022-02-13

What is the probability of getting 7 heads and 7 tails with 14 coin flips?