STATISTICS

Thurs

January 9

• Bell Work:• Turn in Take-Home Quiz

• Notes – Section 5.3 Additional Properties of Binomial Distribution

• Homework due Friday:

A#5.31 pages 203 – 206 #s: 1, 4, 6

Section 5.3 – Additional Properties of the Binomial Distribution

After this section, you will be able to:

1. Make histograms for binomial distributions;

2. Compute µ and σ for a binomial distribution;

3. Compute the minimum number of trials n needed to achieve a given probability of success P(r).

Over the past several chapters, we have explored actual collects of real data, focusing on:

1. The measure of ____________

2. The measure of ____________

3. The nature of the ______________

4. The presence of _______________

5. A ______________ over time.In this chapter, we are focusing on what will _______________ happen.We learned methods for analyzing probability distributions including ________, ____________________, and a probability ___________________.We then looked at a special probability distribution called a _______________.

Stats Review

A binomial distribution tells us the probability of ________________________:

1. Place __________ on the horizontal axis.

2. Place __________ on the vertical axis.

3. Construct a bar over each ________ extending from __________ to _____________. The height of the corresponding bar is ________.

Graphing a binomial distribution

Example graph of a binomial distribution

A waiter at the Green Spot Restaurant has learned from long experience that the probability that a lone diner will leave a tip is only 0.7. During one lunch hour, the waiter serves six people who are dining by themselves.

Make a graph of the binomial probability distribution that shows the probabilities that 0, 1, 2, 3, 4, 5, or all 6 lone diners leave tips.

Example graph of a binomial distribution

PRACTICE: graph of a binomial distribution

Jim enjoys playing basketball. He figures that he makes about 50% of the field goals he attempts during a game. Make a histogram showing the probability that Jim will make 0, 1, 2, 3, 4, 5, or 6 shots out of six attempted field goals.

Mean and Standard Deviation ofA Binomial Distribution

The mean µ of a distribution is also called the _________________.

The standard deviation σ of a distribution is also called the ____________________________.

FormulasFor Any Discrete Probability Distribution

Mean, “Expected Value”

Variance

Standard Deviation

For Binomial Distributions

Mean, “Expected Value”, “Balance Point”

Variance

Standard Deviation, “Measure of Spread”

Computing Mean and Standard Deviation of

A Binomial Distribution is the _______________________________ for the random variable r.

is the __________________________ for the random variable r where:

• ___ is a random variable representing the number of successes in a binomial

distribution;

• ___ is the number of trials;

• ___ is the probability of success on a single trial;

• __________ is the probability of failure on a single trial.

STATISTICS

WednesdayJanuary 22

• Continue Notes – Section 5.3 Additional Properties of Binomial Distribution

• Homework due Thursday:

A#5.31 pages 203 – 206 #s: 8 and 13

Example: Gender SelectionPreviously, we considered a problem involving a preliminary trial with 14 couples who wanted to have baby girls. The result was 13 girls in 14 births.

How much confidence do you have that the MicroSort method of gender selection is effective?

Now assume the sample size includes 100 couples, each of whom will have 1 baby. Also assume that the result is 68 girls among the 100 babies.

a. Assuming the MicroSort gender selection has no effect, find the mean and standard deviation for the numbers of girls in groups of 100 randomly selected babies.

b. Interpret the values from part (a) to determine whether this result (68 girls among 100 babies) supports a claim that the MicroSort method of gender selection is effective.

Example: Gender Selection

Indicator for Unusual Values

For a binomial distribution, it is unusual for the number of successes r to be higher than

________________________ or lower than _______________________.

Sales

Non-profit quotas – volunteers/donations

Medical ScienceQuality Control Risk Management

Traffic ticket

quotas

Example: Junk Bonds (quota)

Suppose you are purchasing junk bonds and consider only companies with a 35% estimate risk of default and your financial investment goal requires four bonds to be “good” bonds in the sense that they will not default before a certain date.

Assume the other bonds in your investment group can default or not without harming your investment plan.

Suppose you want to be 95% certain of meeting your goal (quota) of at least four good bonds.

How many junk bond issues should you buy to meet this goal?

What are junk bonds???

Expressing Binomial Probabilities Using Equivalent Formulas

, where .

Example: Junk Bonds (quota)

A#5.32

DUE:Thursday1/23/14

Pages 203 - 206

#s: 8 and 13