4) The test scores of 32 students are listed below. 32 37 41 44 46 48 53 55 56 5

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 carning a score of 46 and bei at the 46th percentile? 5) In a certain bowl of M&M; candies, there are 10 yellow plain ones peanut ones, 5 green peanut ones, 3 orange plain What is the probability that: ones and 5 green plain ones. a) the selected candy will be green? b) the selected candy will be plain? the selected candy will be both green and plain? d) the selected candy will be either green or plain? e) the selected candy will be green, given that it is plain? 0) the selected candy will be plain, given that it is green? g) If someone selects two candies from the bowl, that they will both be orange? h) If someone selects three candies from the bowl,that that at least one of them is yellow? 6) Suppose that 13% of people are left handed and that 6 people are selected at random, a) What is the probability that exactly 2 of them are left handed? What is the probability that 5 or more are left handed? b) c) What is the mean and standard deviation of the number of left handed people out of the 6 chosen? d) Would it be unusual to have all of the selected people be left handed? 7) A multiple choice test has9 questions each of which has 5 possible answers, only ore of which iscorrect. If Judy, who forgot to study for the test, guesses on all questions what is the prabability that she willanswer exactly 3 questiors correctly?

Explanation / Answer

(4)

For the given data we have:

Sample size, n = 32

Sample mean, m = 67.59

Sample SD, S = 17.28

Standard error of the mean, SE = S/n0.5 = 17.28/320.5 = 3.054

Given percentile, p = 0.46

The corresponding z-score for this p-value is:

z = -0.1

Using the formula:

z = (X-m)/SE

Putting values:

-0.1 = (X-67.59)/3.054

Solving we get:

X = 67.28

So the 46th percentile is 67.28

The difference between scoring 46 and being at the 46th percentile is that the score of 46 has a different percentile value.

46th percentile value is the value which is greater than 46% of all the given sample values.

Hope this helps !

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