final review. the amount of coffee (in ounces) filled in a jar by a machine has a normal...

FINAL REVIEW

The amount of coffee (in ounces) filled in a jar by a machine has a normal distribution with a mean amount of 16 ounces and a standard deviation of 0.2 ounces.

A. The company producing this product can only sell jars that have 16 or more ounces of coffee. What percentage of the jars, in the long run, will not be sellable?


A. The company producing this product can only sell jars that have 16 or more ounces of coffee. What percentage of the jars, in the long run, will not be sellable?

P(X < 16), where the random variable X is the amount of coffee in the jar in ounces.

P(X < 16) = P(Z < )4.

1716

= P(Z < -2.5)

= 0.00621


B. If one were to randomly select 4 jars from the production line, what is the probability of 2 or more jars being rejected?

Let the random variable X count the number of jars out of 4 that will be rejected. From the past problem we know that the probability of finding one jar is 0.00621.

Note: if we assume independence then we have a binomial situation.

So, I will calculate P(X 2) using a binomial function.

P(X 2) = 0.00029


C. If one were to randomly select 4 jars from the production line, what is the probability that the average amount of coffee in the four jars is 16.5 ounces or less?

Since we are considering the average amount of coffee in the four jars, it is a sampling distribution problem. We want P(X < 16.5).

So, I will calculate P(X < 16.5) = P(Z < ) = P(Z < -2.5) = 0.00621.4

4.175.16


D. If one were to randomly select 4 jars from the production line, what is the probability that the amount of coffee in all four jars is 17 ounces or more?

In this case I want all four jars to have more than 17 ounces. Let the random variable X be the amount of coffee in a jar in ounces. The

P(X > 17) = 0.5 by looking at the graph. I want to calculate

P(X> 17 and X > 17 and X > 17 and X > 17)


D. If one were to randomly select 4 jars from the production line, what is the probability that the amount of coffee in all four jars is 17 ounces or more?

P(X > 17) = 0.5 by looking at the graph. I want to calculate

P(X> 17 and X > 17 and X > 17 and X > 17). Assuming independence between the events, I can rewrite the probability statement as

P(X>17)*P(X > 17)*P(X > 17)*P(X > 17) = (0.5)4 = 0.0625.


E. If one were to randomly a jar from the production line, what is the probability that the average amount of coffee in the jar is more than 17.4 ounces or less than 16.6 ounces?

Notice we want to calculate

P(X< 16.6 ounces or X > 17.4 ounces). The two events are disjoint. I also notice that

P(X< 16.6 ounces or X > 17.4 ounces) = 1 - P(16.6 < X < 17.4)

1 - .68 = .32

During the last election about 110 million registered voters voted for the presidency. Suppose that 45% of those registered voters voted for George Bush. If we gathered a simple random sample of 1000 voters what is the probability that 400 or less voted for George Bush? Use continuity correction to approximate the probability.

= 1000(.45) = 450

= 15.73 )55)(.45(.1000Binomial parameters

P(X < 400) where X is the binomial random variable.

P(X< 400) P(Z < ) = P(Z < -3.15)

= 0.000873.15

4505.400

What is the purpose of creating a confidence interval?

To estimate the population mean with an interval.

A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a given day. The distribution is as follows:

Number sold in one day 0 5 10 15 20

Probability of selling x .05 .2 .30 .35 .1

Find the number of cheesecakes that this local bakery expects to sell in a day on average in the long run.

= 0(.05) + 5(.2) + 10(.30) + 15(.35) + 20(.1)

= 11.25 cheesecakes per day on average.

Lets say that the probability of being born a girl is 0.55 and the odds of being born a boy are 0.45. Let the random variable X count the number of girls for a family of four children.

A. Write out the sample space for the random variable X.

X = {0, 1, 2, 3, 4}

B. Write the probability distribution for the random variable X

X 0 1 2 3 4

P(x) .041 .200 .368 .299 .092

THE END?

final review. the amount of coffee (in ounces) filled in a jar by a machine has a normal...

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