Question

• Example 1: A shipment of 80 burglar alarms contains four that are defective. If three from the shipment are randomly selected and shipped to a costumer, find the probability that the costumer will get exactly one bad unit. • Example 2: It is known from experience that 1.4 percent of the calls received by a switchboard are wrong numbers. Use the Poisson approximation to the binomial distribution to determine the probability that among 150 calls received by the switchboard two are wrong numbers. • Example 3: The number of complaints that a dry-cleaning establishment receives per day is a random variable having Poisson distribution with $\lambda = 3.3$. Use the formula for a Poisson distribution to find the probability that it will receive only two complaints on any given day.

          • Example 1: A shipment of 80 burglar alarms contains four that are
defective. If three from the shipment are randomly selected and shipped
to a costumer, find the probability that the costumer will get exactly one
bad unit.
• Example 2: It is known from experience that 1.4 percent of the calls
received by a switchboard are wrong numbers. Use the Poisson
approximation to the binomial distribution to determine the probability
that among 150 calls received by the switchboard two are wrong
numbers.
• Example 3: The number of complaints that a dry-cleaning
establishment receives per day is a random variable having Poisson
distribution with $\lambda = 3.3$. Use the formula for a Poisson distribution
to find the probability that it will receive only two complaints on any
given day.

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• Example 1: A shipment of 80 burglar alarms contains four that are
defective. If three from the shipment are randomly selected and shipped
to a costumer, find the probability that the costumer will get exactly one
bad unit.
• Example 2: It is known from experience that 1.4 percent of the calls
received by a switchboard are wrong numbers. Use the Poisson
approximation to the binomial distribution to determine the probability
that among 150 calls received by the switchboard two are wrong
numbers.
• Example 3: The number of complaints that a dry-cleaning
establishment receives per day is a random variable having Poisson
distribution with λ = 3.3. Use the formula for a Poisson distribution
to find the probability that it will receive only two complaints on any
given day.

Added by John B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Kari Hasz

03/10/2023

Step 1

The formula for the binomial distribution is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success. Show more…

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Example 1: A shipment of 80 burglar alarms contains four that are defective. If three from the shipment are randomly selected and shipped to a costumer, find the probability that the costumer will get exactly one bad unit. Example 2: It is known from experience that 1.4 percent of the calls received by a switchboard are wrong numbers. Use the Poisson approximation to the binomial distribution to determine the probability that among 150 calls received by the switchboard two are wrong numbers. Example 3: The number of complaints that a dry-cleaning establishment receives per day is a random variable having Poisson distribution with lambda =3.3. Use the formula for a Poisson distribution to find the probability that it will receive only two complaints on any given day. Example 1: A shipment of 80 burglar alarms contains four that are defective. If three from the shipment are randomly selected and shipped to a costumer, find the probability that the costumer will get exactly one bad unit. Example 2: It is known from experience that 1.4 percent of the calls received by a switchboard are wrong numbers. Use the Poisson approximation to the binomial distribution to determine the probability that among 150 calls received by the switchboard two are wrong numbers. - Example 3: The number of complaints that a dry-cleaning establishment receives per day is a random variable having Poisson distribution with 1 = 3.3. Use the formula for a Poisson distribution to find the probability that it will receive only two complaints on any given day.

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Transcript

00:01 In this situation, we have four different problems that we're going to solve.

00:06 So in each of these problems, we have a binomial situation.

00:11 So in our first, we have a probability of 5%, a sample size of 100, and we are asked to find the probability that x is greater than 5, probability that x is greater than 10, and the probability that x is greater than 15.

00:27 Now we're asked to use a binomial distribution calculator.

00:32 So you can do that by simply googling binomial distribution calculator and entering in your values.

00:38 You can use your graphing calculator, but you have to have an extra step.

00:44 So if you use a graphing calculator as your binomial distribution calculator, you'll go to second vars.

00:50 You'll go to b -b -b -b -b -c -d -f.

00:56 And then you'll enter your values in just like you would a distribution calculator on the internet, but then you're going to need to remember to subtract your values from one.

01:06 So whichever calculator you choose to use, you're going to end up with the following values.

01:16 For number two, now our probability is 2%.

01:19 We have a sample of 50, and we're finding the probability that x is greater than 1, probability that x is greater than 2, and the probability that x is greater than 3.

01:30 Tasked with using a binomal distribution calculator.

01:37 And you can again use the calculator on the internet or you can use your graphing calculator, but remember to subtract your answer from one.

01:49 So if you use the graphing calculator, you have to remember because the calculator is going to tell you to the left and you want to the right.

01:58 So in the case of number two, we have 0 .264.

02:04 We have 0 .0784 and 0 .178...

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