Follow-Up on Yesterday’s last problem. Then we’ll review. Sit in the groups below Brendan and Tim are playing in an MB golf tournament. Their scores vary

Follow-Up on Yesterday’s last problem. Then we’ll review. Sit in the groups below

Brendan and Tim are playing in an MB golf tournament. Their scores vary as they play the course repeatedly. Tim’s score X has the N(110, 10) distribution. Brendan’s score Y varies from round to round according to the N(100, 8) distribution.

If they play independently, what is the probability that Tim will score lower than Brendan and thus do better in the tournament?

We found the distribution of X – Y to be N(10, 12.80)

We want to find the Probability that Tim’s score is less than Brendan’s (i.e. P(X<Y) which is the same as the P(X-Y<0).

Let’s use a z-score the determine this probability.

Ways to Review• Read. Reread either parts of the chapters or the 5 steps to a 5

lesson.

• Look over the problems that we do in class today and on the review game.

• Make sure that your HW is completed (HW 34-39 will be collected). Check solutions online.

• Doing some extra review problems won’t hurt either.

• Make sure that you bring your formula sheet to the test tomorrow.

Part 1: Review Problem Set• Get in the following groups. I split you up so you would work with people

that you might not normally work with. It was randomly assigned though.

• Look at the MC review set from 5 steps to a 5. Same set that was assigned last night. Work with your group to answer all of the multiple choice questions that you did not do last night.

• Also complete the following Free Response Questions: 6, 9, 12

• Your team has an answer sheet on your desk as well.

• We will then play a review game for the last half of class.

Review Game for a HW Pass!

Review Game: Question 1


Answer: AKey Concept: The sample space is what is possible in a situation.



Answer: AKey Concept: Be careful with percents and decimals. To turn a decimal to a percent, movethe decimal two spaces to the right.



Answer: CKey Concept: The probability is 50% (0.2 + 0.3) so over the long run we would expect approx this proportion



Answer: CKey Concept: P(pink U no fragrance) = 120/400 + 134/400 – 16/400

Don’t forget to subtract the “overlap” they are not mutually exclusive.



Answer: CKey Concept: independence means that the probability of A does not impact the prob. of B.



Answer: BKey Concept: The prob that a doctor doesn’t carry malpractice insurance is 0.18.

Because of independence, if we want to calculate the prob that all 3 doctors do carry insurance,The calculation would be 0.82*0.82*0.82 = 0.823 = 0.551 all the rest of the time at least one doctorDoes NOT carry insurance

So the prob that at least one of the 3 doctors does NOT carry insurance would be 1 – 0.551 = 0.449



Answer: BKey Concept: In the first deck, the prob is not independent. Getting a red card on the firstCard impacts (lowers) the prob of getting a red card on the second draw (12/51 as opposedTo 13/52 with the first card). The probabilities are 13/52 for both red cards on the second deck.



Answer: BKey Concept: discrete means countable. Continuous means not countable



Answer: AKey Concept: Expected value is the sum of X*p(x). Make a table with outcomes and prob.

2(0.3) + 4 (0.1) + 0 (0.6) = 1


Answer: BKey Concept: 0.4 + 0.1 = 0.5



Answer: CKey Concept: The mean of X is 1.5. Take each x-value and subtract the mean. Then square that Value and multiply it by P(x) for each data point. Find the sum (which is the variance). Take the squareRoot for the std. deviation. (0-1.5)2(0.1) + (1-1.5)2(0.4)… etc. Then take the square root.



Answer: CKey Concept: Density curves have areas of 1. So the ten minutes must have a height of 0.1 (since 10*0.1=1). Therefore the P(6 < X < 8) = 2 *0.1 = 0.2



Answer: BKey Concept: remember, we can’t just add or subtract std. deviations. We can only use the ruleFor variances. So the variance is 1.22 = 1.44. The variance of X-Y = var2+ var2 = 1.22 + 1.22 = 2.88.The square root of this is the std deviation = 1.6970



Answer: AKey Concept: The mean of c = 500 + 10(200) using the rules for means.To find the standard deviation of C, use the rules for variances. The variance of X is 400.

So b2(variance) = 102 400 = 40,000 the square root of this is 200.



Answer: CKey Concept: For standard deviation we would need to know if X and Y were independent beforeWe could do part c.



Answer: CKey Concept: Calculate a z-score and look it up on the z-table. (700-530)/120= z = 1.416.

Prob from the z-table is 0.922. We want it to EXCEED $700 so we are looking for the right tail.So we do 1- 0.922 = 0.0778



Answer: BKey Concept: Find the expected value 1(0.1) + 2(0.2) + 3(0.3) + 4(0.2) + 5(0.1) + 6(0.1)

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Follow-Up on Yesterday’s last problem. Then we’ll review. Sit in the groups below Brendan and Tim are playing in an MB golf tournament. Their scores vary