Did you read my tips on how to study and learn Stat 1000?  If not, here is a link to those important suggestions:

Did you read my Calculator Tips?  If not, here is a link to those important suggestions:

Did you see my tips for Assignment 1? Click here.

Did you see my tips for Assignment 2? Click here.

Did you see my tips for Assignment 3? Click here.

To type in formulas you are using and to show your numbers subbed into the formulas you can click the Equation Editor button in the toolbar that looks like the Sigma Summation symbol (you have to click the "..." other options button to see the sigma formula input button.  Then click the various buttons to make your fractions and enter the symbols.  However, the Equation Editor is extremely slow and clunky.  Personally, I would never use it.  Just type ordinary text explaining what you are doing if you think you should show some work.

This is two-way table stuff from Lesson 5 similar to my questions 4 and 6.

Be careful! You are being asked for first light Green OR second light Red.  Use the check-mark method I teach in Lesson 5.  Check off all the outcomes where first light is Green.  Check off all the outcomes where second light is Red (some outcomes will get two check marks).  If this had been "and," you would have added all the probabilities with two check marks.  But, this is "or," so you add up all the probabilities with one or more check marks.

This is just saying X = number of red lights.

I tell you the definitions of parameters and statistics at the start of Lesson 4 of my book and I repeat them again in Lesson 7 and illustrate with my question 1.

Note that 110 is the count, X, from a sample.  Since it is the count from a sample, it must be a ...?

Lesson 6.  If you are ever asked to decide if a particular situation is binomial or not, remember, to be binomial, four conditions must be satisfied:

1. There must be a fixed number of trials, n.
2. Each trial can have only two possible outcomes, success or failure, and the probability of success on each trial must have a constant value, p.
3. Each trial must be independent.
4. X, the number of successes, is a discrete random variable where X = 0, 1, 2, ... n.

• If you are reading off numbers from a randomly selected row in the random number table, note that every row has 40 digits.  That is like 40 trials looking for whatever digit you may be looking for.  What is the probability that, at any moment on the table, the next digit is a 0, or a 1, or a 2, etc..
• If you are selecting objects, are you sampling with replacement (independent trials) or without replacement (dependent trials)?
• If you are given a Normal population, but are selecting a sample of size n, and want to see how many of them are greater than 62 (for example), THAT IS A BINOMIAL DISTRIBUTION!  You can use Table A to find what proportion are greater than 62.  That is your p.  Each trial, the person/thing either is greater than 62, or they are not.  And the chance they are greater than 62 is p, the proportion you shaded on the bell curve.
• If you are ever conducting trials until you get a desired result, that will never be binomial because you do not have a fixed number of trials, n.  For example, if I am rolling a die until I get a six and X= the number of rolls until I get a six, that is not binomial, because there are no fixed number of trials, n.
• Look at my solutions to your practice midterms (if you have them).  There are similar questions in both exams which will give you more insight.
  

Lesson 6.  I introduce the formula for mean and standard deviation of a binomial distribution in my question 7.  Note that they are asking for the variance, not the standard deviation.  That is a little neater since the variance is np(1-p).

Be careful that you are using the correct n and p for each question since they keep switching which colour light, and how many days they are talking about.  Note that n is the TOTAL number of intersections the student has encountered during the time period.

This is Lesson 7 stuff.  You have to always be asking yourself, "Is the problem talking about one individual score X? Or, is it talking about the mean of n scores, x-bar?"  If it is talking about just one score X, is X normally distributed?  If it is talking about the mean of n scores, x-bar, can we assume x-bar is normally distributed?  Why or why not?  If we can assume these are normally distributed, then be careful to use the proper standardizing formula.  Either the X-Bell Curve formula or the x-Bar Bell Curve formula.

Look at my questions 4 through 7 in Lesson 7 for examples.  Especially take note of my questions 6 and 7 if they give you a total amount in a question as they do in part (c).

Be careful in part (d).  They are talking about the mean of a sample of some size n (the value of n varies for different students).  Thus, you must compute the mean of x-bar and the standard deviation of x-bar, which are mu and sigma divide by square root n first, then use those values for your 68-95-99.7 rule.  Make sure you put the smaller answer first.

When computing things like sigma/ square root n, make sure you round off to NO LESS THAN 4 decimal places.  Better yet, store the exact value in the memory of your calculator. 

In part (c), be sure that you do not round off your answers for the sample mean too much.  Again, use at least 4 decimal places in your answers.  Better yet, don't even round off at all.  If the total is 179 and n is 13, just say x-bar is 179/13 and leave it like that.  Put 179/13 in for x-bar in your standardizing formula.  The calculator will handle that just fine, and you will get a more accurate answer for z.

Approach this just like the previous question.  Ask yourself the same questions.