# c. If you roll the die six times what are your chances of getting at least one d. roll.

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1 1. Find the area under the normal curve: a. To the right of 1.25 ( )/2= b. To the left of ( )/2=34.46 c. To the left of 0.80 ( )/2= d. Between 0.40 and 1.30 for z=1.30, area=80.64 for z=0.40, area=31.08 ( )/2=24.78 e. Between and 0.90 for z=-0.30, area=23.58 for z=0.90, area=63.19 ( )/2= = f. Outside of -1.5 and 1.5 ( )= You have a standard 6-sided die. Compute the following and explain your answers. a. If you roll the die 1/6 = 16.67% b. 1/6 + 1/6 = 2/6 = 33.33% c. If you roll the die six times what are your chances of getting at least one P(6) = 1 P(No 6) P(No 6) = == P(6) = = P(6) = 66.51% [Addition Rule. 14.2] [Opposite Chance. 14.4] d. roll. (1/6) x 1 x 1 x (1/6) = 1/36 = 27.78%

2 Note: Rolls two and three can have any outcome and not affect the question at hand. Therefore for those any of the 6 numbers out of the 6 possible outcomes are acceptable. [Multiplication Rule, 13.3] 3. If the average is 535 and the SD is 100, estimate the 95 th percentile. For area of 90%, z=1.65. Translated back, this score is above average by 1.65x100=165. The 95 th percentile is = You have a standard 52-card deck. Compute the following probabilities and explain your answers. a) The first card you draw from the deck is an ace. 4/52 = 7.69% b) You draw two cards without replacement, the first one is a heart and the second is a heart. (13/52) x (12/51) = 5.88% c) You draw two cards with replacement. That is you draw a card, put it back in the deck then draw another card. What are the chances the 2 cards are the exact same card (eg. Queen of hearts, or jack of spades)? (52/52) x (1/52) = 1/52 = 1.92% -This is an example of one you have to think about in some other way besides simple addition or multiplication rule. One way to think about it is you have already drawn the first card, what are the odds the second card matches the first? For the first card you can pick anything (52/52) and the second card must match the first (1/52) 5. A group of researchers is trying to find out whether the age of a car affects its braking capability. They test the minimum stopping distance of a group of 6 cars of different ages. The results are below: Car age (months) Minimum Stopping distance at 25 mph (feet)

3 a. Find the correlation coefficient for the data in the table above. b. x (x-ave) 2 standard units x y (y-ave) 2 standard units y prod x*y Ave= 27 Ave= SD= Sqrt(968/6) =12.70 SD= Sqrt(862.8/6) = r = c. How does r change if we measure the stopping distance in meters rather than feet? (1 foot is about 0.3 meters) r stays the same. d. A different group of researchers found the average age of cars in each of the 50 states and the average stopping distance in each state. They also find a positive correlation. In this study, it fair to say that the age of a car is the cause of greater stopping distance? Nope, in this case we have an ecological correlati older are the same cars that have further stopping distances. 6. You flip a coin. If it lands on heads you draw a card from a standard deck, if it lands on tails you roll a die. Calculate the probability of the following and explain. [note: unless otherwise stated assume you are calculating the probability of the events occurring before the coin is even flipped] a) You get heads and you roll a 5 on the die. 0%. The two events are mutually exclusive. That is the coin landing on heads prevents you from rolling the die at all. b) You draw an ace from the deck. (1/2) x (4/52) = 1/26 = 3.85% c) You either roll a 2, or draw a 2 from the deck. (1/2)x(1/6) + (1/2)x(4/52) = 12.17%

5 A B C D Final Score

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