Unit HW 3 Conditional probability and Statistics PDF

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Unit homework number 3 that deals with "Conditional Probability and Statistics"....

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UNIT HOMEWORK #3 –CONDITIONAL PROBABILITY, STATISTICS YOU MUST SHOW ALL WORK TO RECEIVE CREDIT 1) You draw 2 cards from a standard deck of cards without replacement.

a) What is the probability that the second card is a two given that the first card is a two? Cards #2 = 4/52 P(second card is #2) = 3/51 = 1/17 b) What is the probability that the second card is a face card given that the first card was a jack? Total face cards= 12/52 P(second card is face) = 11/51 c) What is the probability that the second card is a ten given that the first card is a three? Total # of ten’s = 4 Total cards after first card = 51 = 4/51 2) A local lottery costs $5 a ticket, and there are 5000 tickets sold. There is one first prize for $1000, three second prizes of $100 each and ten third prizes of $25 each. You decide to purchase one ticket. What are your expected winnings? Make sure you show all work

X P(x)

995 1/5000

95 3/5000

20 10/5000

-5 2493/2500

= 995(1/5000)+95(3/5000)+20(10/5000)+(-5)(2493/2500) = 0.199+0.057+0.04-4.986 =expected winnings = -$4.69, not fair

3) Answer the following questions based on the set of numbers: 11, 14, 12, 12, 13, 9

a) Find the standard deviation. Be sure to show the work. x x- mean 11 11-11.83= -0.83 14 14-11.83= 2.17 12 12-11.83= 0.17 12 12-11.83= 0.17 13 13-11.83= 1.17 9 9-11.83= -2.83 Total: 71 0.02

(x-mean)^2 0.6889 4.7089 0.0289 0.0289 1.3689 8.0089 14.8334

S^2= 14.8334/6-1 = 14.8334/5 = 2.96668 S = sqrt 2.96668 = 1.722405295 Standard deviation: 1.72 b) What does standard deviation tell us about the data? Standard deviation tells you the average amount that each sample number from the data is away from the mean. c) If the above data set included another number, say 98, how will that affect the standard deviation? No need to calculate the standard deviation The mean for the sample numbers will change, becoming higher. With the addition of the number 98 the total is 169, with 7 numbers total instead of 71 with 6 numbers. 4) Why is it that if A and B are independent events, P(A/B)= P(A)? If A and B are independent events, then P(A/B)=P(A) because event A is not affected by the outcome of event B, the knowledge of the first event does not affect the second event. 5) A large group of students took a test in Finite Math where the grades had a mean of 72 and a standard deviation of 4. Assume that the distribution of these grades is approximated by a normal distribution and that passing the test is a 65. a) What percent of students scored higher an 81 or higher? z= x-/  z= 81-72/4= 9/4 = 2.25 A(2.25)= 0.9946 1- 0.9964= 0.0054 = 0.54% b) What percent of students failed the test? z= x-/  z= 65-72/4 = -7/4= -1.75 A(-1.75)= 0.0401 = 4.01% c) What percent of students scored between a 70 and 75?

z= x-/  = 70-72/4= -2/4= -0.5 A(-0.5)= 0.3085 z= x-/  = 75-72/4= 3/4= 0.75 A(0.75)= 0.7734

0.7734-0.3085= 0.4649 = 46.49%

d) What happens when you try to find the percent of students that scored less than a 40? When attempting to do normal distribution, z= x-/ , you get -32/4= -8. The table of standard normal probabilities for negative z-scores does not got up to 8 so u=you cannot find A(-8), so you cannot find the percent of students that scored less than a 40. 6) Do you find conditional probability problems challenging? Have you tried watching the videos on canvas and has it helped? I am confident when doing conditional probabilities but sometimes have trouble differentiating what to towards the, whether I have to subtract from one or the answer stays as is. I did watch the videos on canvas and took notes, the videos on canvas always help me more than the textbook, so I always find them useful....