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## STAT 200 PSU Quiz 3

by: kimwood Notetaker

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# STAT 200 PSU Quiz 3

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STAT 200 PSU Quiz 3
COURSE
PROF.
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TYPE
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PAGES
6
WORDS
KARMA
50 ?

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This 6 page Study Guide was uploaded by kimwood Notetaker on Friday November 6, 2015. The Study Guide belongs to a course at a university taught by a professor in Fall. Since its upload, it has received 61 views.

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Date Created: 11/06/15
1. Decide if the probability described is a subjective (personal) probability or a relative frequency probability:  A quarter is flipped 2000 times and results in 500 heads. The 25% (500/2000) chance of heads is a A) subjective probability.  B) relative frequency probability.  Points Earned: 1.0/1.0 2. A statistics class has 4 teaching assistants (TAs): three female assistants (Lauren, Rona, and Leila) and  one male assistant (Josh). Each TA teaches one discussion section. A student picks a discussion section. The two events W = {the TA is a woman} and J = {the TA is Josh} are A) independent events.  B) disjoint (mutually exclusive) events.  C) each simple events.  D) None of the above.  Feedback: These events are mutually exclusive since both events cannot occur at the same time. Points Earned: 1.0/1.0 3. In the past five years, only 5% of pre­school children did not improve their swimming skills after taking a  Beginner Swimmer Class at a certain Recreation Center. What is the probability that a pre­school child  who is taking this swim class will improve his/her swimming skills? A) 5%  B) 10%  C) 95%  Feedback: If 5% did not improve then 95% did improve since you can either improve or not improve. Points Earned: 1.0/1.0 4. Lauren wants to wear something warm when she leaves for class. She reaches into her coat closet  without looking and grabs a hanger. Based on what she has in her coat closet, she has a 30% chance of  picking a sweater, a 50% chance of picking a coat, and a 20% chance of picking a jacket. What is the  probability that she will pick a sweater or a coat? A) 15%  B) 30%  C) 50%  D) 80%  Feedback: 30% plus 50% = 80%. These events are added since mutually exclusive and follow the  additive rule. Points Earned: 1.0/1.0 5. Decide if the probability described is a subjective (personal) probability or a relative frequency probability:  A recent college graduate claims he only has a 30% chance of finding a job in the next two months. The  chance of 30% is a A) subjective probability.  B) relative frequency probability.  Points Earned: 1.0/1.0 6. For the following statement, determine if it is true or false. If two events A and B are independent, they  must also be mutually exclusive. A) True  B) False  Feedback: False; independent does not imply mutually exclusive, only that the outcome of the one event  does not affect the probability of the outcome for another event. Points Earned: 1.0/1.0 7. For the following statement, determine if it is true or false. If two events A and B are mutually exclusive,  they must also be independent. A) True  B) False  Feedback: False; Just the opposite: if mutually exclusive then dependent. Think of the events being Male and being  Female. These two events are mutually exclusive since you can only be in one of the events. However,  knowing that you are in event Male automatically disqualifies you from being in event Female so the  P(male) is dependent on P(female) and vice­versa Points Earned: 1.0/1.0 8. A standard 52­card deck is shuffled and 2 cards are picked, without replacement, from the top of the  deck. The probability that the first card is a face card (Jack, Queen, King) and the second card is not a  face card is A) 5.3%  B) 17.8%  C) 18.1%  D) 59.2%  Feedback: P(Heart) times P(heart) = 12/52 times 40/51 = 18.1% Points Earned: 0.0/1.0 9. A card is drawn at random from a standard 52­card deck. The conditional probability that the card is a 2  given that a 2 or a 3 was drawn is A) 20.0% (1/5)  B) 25.0% (1/4)  C) 33.3% (1/3)  D) 50.0% (1/2)  Feedback: P(2 | 2or3) = 1/2; there are 8 twos and threes, then out of those there are 4 2s: 4/8 = 1/2 Points Earned: 0.0/1.0 10. Two standard 52­card decks are shuffled and two cards are picked at random, one card from each deck.  The probability that two Hearts are drawn is A) 5.9%  B) 6.25%  C) 25.0 %  D) 50.0%  Feedback: P(Heart) times P(heart) = 13/52 times 13/52 = 6.25% Points Earned: 0.0/1.0 11. From a Class Survey, approximately 32% of the students responding said that they have driven a vehicle  while under the influence of drugs or alcohol. If you got into a car with two students from this class, what  is the probability that both of them would have previously driven while under the influence? A) 64%  B) 32%  C) 22%  D) 10%  Feedback: The probability that both have driven while under the influence is equal to 0.32 times 0.32  which equals 10% Points Earned: 0.0/1.0 12. Which of the following is the sample space when 2 coins are tossed? [H = Head, T = Tail] A) {H, T, H, T}  B) {H, T}  C) {HH, HT, TH, TT}  Feedback: The answer is {HH, HT, TH, TT}. When two coins are tossed, for either coin the outcome is a  Head or a Tail. Thus there are 2  = 4 possible outcomes. Points Earned: 0.0/1.0 13. According to the Penn State Fact Book for Enrollment by Ethnicity Fall 2005 [University Park], in a class  of 30 students, there would be 17 males and 13 females. Let us say that out of these 30 students five are  A students, three of which are males. If a student is chosen at random, what is the probability of choosing a male or an A student? A) 19/30  B) 11/15  C) 17/180  Feedback: You are asked to find P(M or A) = P(M) + P(A) ­ P(A and M). Drawing a Venn Diagram such  as the one found at See Venn helps tremendously in seeing how to solve this problem. P(M) = 17/30,  P(A) = 5/30 and (M and A) = 3/30. Substituting these into the equation for P(M and A) results in 17/30 +  5/30 ­ 3/30 = 19/30. Points Earned: 0.0/1.0 14. Elizabeth has just put 4 new spark plugs in her car. For each spark plug, the probability that it will fail in  the next 50,000 miles is 1/100 (which is 0.01), and is independent from one spark plug to the next. What  is the probability that none of the spark plugs will fail in the next 50,000 miles? A) (0.01)(0.01)(0.01)(0.01)  B) 1­ (0.01)(0.01)(0.01)(0.01)  C) (0.99)(0.99)(0.99)(0.99)  D) 1­ (0.99)(0.99)(0.99)(0.99)  Feedback: Probability of not fail is 0.99 and for all four plugs independence means multiply so (0.99) (0.99)(0.99)(0.99). We do not use 1 minus .99*.99*.99*.99 because the complement to none of the spark  plugs fail is that at least one spark plug fails. Points Earned: 0.0/1.0 15. A medical treatment has a success rate of 0.8. Two patients will be treated with this treatment. Assuming  the results are independent for the two patients, what is the probability that neither one of them will be  successfully cured? A) 0.5  B) 0.36  C) 0.2  D) 0.04  Feedback: Probability of cured is 0.8 so probability of not cured is 0.2. Independence means multiply so  probability that both are not cured is 0.2*0.2 = 0.04 Points Earned: 0.0/1.0

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