1) Baseball. For simplicity sake, assume the probability of a good batter getting a hit during an atbat is .300
Why is this question a Binomial? Define a “success”. What is n and p?
If a batter has 4 (official) at bats in a game, what is the probability of getting at least one hit?
Probability of no hits (4 at bats)?
Probability of going 4 for 4?
What is the mean number of hits in a game (for a good batter) and the standard deviation?
2) Staying with the example in the previous question. What is the probability of a batter getting at
least one hit in a game for 10 games in a row?
Why is this question Binomial? Define a “success”. What is n and p?
Probability of getting at least 1 hit in a game for 20 games in a row?
56 games in a row?
What is the value of µx, and what does it mean?
3) The rate of potholes on a major street has a Poisson distribution with a rate of 3 potholes per
mile. Find in a 2 mile stretch of that road the probability that
The rate is:
The number of intervals is:
There are 4 potholes
There is more than 1 pothole
Between 5 and 7 potholes (inclusive)
Find µx
Find σx
4) Performance on SAT exams is normally distributed with a mean of 509 and a standard deviation
of 112. If an SAT test taker is chosen at random, what is the probability that their score is
At least 509
Between 500 and 700
Greater than 650
Homework,
Section 7.1, #28, #30, #34, #44,
Section 7.2, #34, #36
5) The delay in arrival (how late) of a commercial air flight is distributed normally with mean 8
minutes and standard deviation of 14 minutes.
Draw and calculate the probability of being more
than 30 minutes late
Draw and calculate the probability of being no
more than 10 minute late
Draw and calculate the probability of a flight
landing within 5 minutes of its scheduled time
Your plane lands 20 minutes late, in what
percentile is that?
Draw and calculate: Planes that land later than
80% of flights are how late?
Draw and calculate: Planes that land earlier than
80% of flights are how early?
Draw and calculate: if an unusual event is one that Draw and calculate: if an unusual event is one that
happens less than 1% of the time, what would
happens less than 5% of the time, what times
define an unusually early arrival?
would define either an unusually early or late
arrival?
Some thoughts about Chapter 6:
Three main topics:
“Generic” discrete probability distribution
Example: Section 6.1 Question #45
Be able to calculate the probability of specific outcomes
Be able to find the mean and standard deviation (use the calculator for this)
Binomial discrete distribution
You do NOT need to be able to use the “tables” (see Example 6.15)
Example: Section 6.2 Questions #33, 35
Be able to use calculator to solve binomial probabilities
Be able to find mean and standard deviation (use formula)
Poisson distribution
Example: Section 6.3, Questions #25, 27
Be able to use calculator to solve Poisson probabilities
Be able to find mean and standard deviation (use formula)
Some thoughts on Chapter 7:
Using Normalcdf
Given the mean and standard deviation of a normal distribution, be able to find the
probability of a valuing falling within a given range.
Be able to do the previous with a z-score (which simply means µx= 0, σx= 1)
You do NOT need to be able to use a table (Table A.2)
Using InvNormal
Be able to use the InvNormal to find the value of X that has an area (probability) to
the left or right.
Do the previous but with a z-score (find a zα where α is the area to the RIGHT of z)
Note: the calculator will automatically convert values to z-scores. So we won’t be doing
that unless I specifically ask you to find a z-score.
*** HUGE Understand and apply the Central Limit Theorem (it’s apply to 𝑥̅ )
Only if we have time (probably won’t):
Evaluating Normality
Using CLT for probabilities
Reminders on Regressions
Be able to calculate the regression line (given the X & Y data)
Interpret the X coefficient
Interpret the Y-axis intercept
Find and interpret the X-axis intercept
Interpret the correlation coefficient, r
Interpret the coefficient of determination, r2
Be able to find the predicted y’s based on the x’s
Be able to find the residuals
Be able to plot the residuals (against the X variables) and identify any problem
Be able to make a prediction of the Y given the X
Be able to predict a change in Y given a change in X
Be able to describe a necessary X given a desirable Y