4) The test scores of 32 students are listed below 32 37 41 44 46 48 53 55 56 57

Question

4) The test scores of 32 students are listed below 32 37 41 44 46 48 53 55 56 57 59 63 65 66 68 69 70 71 74 74 75 77 78 79 80 82 83 86 89 92 95 99 a)Find P46 b) What is the difference between earning a score of 46 and being at the 46th percentile? 5) In a certain bowl of M&M; candies, there are 10 yellow plain ones, 6 orange peanut ones, 6 yellow peanut ones, 5 green peanut ones, 3 orange plain ones and 5 green plain ones. What is the probability that: a) b) c) d) e) 2 8) h) the selected candy will be green? the selected candy will be plain? the selected candy will be both green and plain? the selected candy will be either green or plain? the selected candy will be green, given that it is plain? the selected candy will be plain, given that it is green? If someone selects two candies from the bowl, that they will both be orange? Ir someone selects three candies from the bowl ,that that at least one of them is yellow? 6) Suppose that 13% of people are left hanced and that 6 people are selected at random.. What is the probability that exactly 2 of them are left handed What is the probability that 5 or more are left ha a) b) t is the mean and standard deviation of the number of left handed people out of the 6 chosen? Would it be unusual to have all of the selected people be left handed? d) Judy, who forgot exactly 3 questiors correctly? test has9 questions each of which has 5 possible answers, only ore of which to study for the test, guesses on all questions what is the probability that she will answer

Explanation / Answer

#4

a)

k=46 and n=32.

P=k*n/100 = (46)(32)/100 = 14.72 15th value

Therefore, P46 is the 15th value of the sorted data.

P46 = 68

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b)

Earning a score 46 means a student's score is 46 while being 46th percentile means 46% of the students scored below that score.

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#5

a) P(Green) = 10/35 = 0.2857

b) P(Plain) = 18/35 = 0.5143

c) P(Green and plain) = 5/35 = 0.1429

d) P(Green or plain) = P(Green) + P(Plain) - P(Green and plain) = 10/35 + 18/35 - 5/35 = 23/35 = 0.6571

e) P(Green|Plain) = P(Green and plain)/P(Plain) = (5/35)/(18/35) = 0.2778

f) P(Plain|Green) = P(Green and plain)/P(Green) = (5/35)/(10/35) = 0.5

g) P(Orange and Orange) = P(first orange)P(Second orange|First orange) = (9/35)(8/34) = 0.0606

h) P(Atleast one yellow) = 1 - P(none is yellow) = 1 - (19/35)(18/34)(17/33) = 0.8519

Plain Peanut Total Yellow 10 6 16 Orange 3 6 9 Green 5 5 10 Total 18 17 35

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