1. The Gagosian art gallery in New York City has 20 stored paintings but has jus
ID: 3202498 • Letter: 1
Question
1. The Gagosian art gallery in New York City has 20 stored paintings but has just made room to display several of them. Seven paintings will be randomly selected and offered to the public for sale
a. How many different collections of 7 paintings are possible
b. Suppose 10 of 20 stored works are by the same local artist. What is the probability that all 7 of the selected paintings will be by this artist
c. The featured room in the gallery receives the most attention, and the order in which the paintings are displayed in this room is related to buyer interest. Suppose the 7 selected paintings will be placed in this featured room. How many different arrangements are possible
My answers:
a. 20C7 = 77520
b. 10C7 * 10C0 = 120 / 20C7 = 0.0015
c. 7! = 5040
2. A university library is preparing a display case of bookes written by faculty members. There are 25 new faculty books, but there is room for only 10 in the display case. Suppose 10 books are selected at random
a. How many different faculty book collections can be displayed
b. If 15 of the new books are written by faculty members from the College of Science and Technology, what is the probability that all 10 displayed books are written by faculty members from this college
c. If none of the 10 displayed books is written by faculty members from the College of Science and Technology, is there any evidence to suggest the selection process was not random? Justify your answer
My answers:
a. 25C10 = 3268760
b. 15C10 * 10C0 = 6435 / 25C10 = 0.0019
c. 10C0 * 15C7 = 6435 and I have no clue in how to answer "Justify your answer"
3. Although caffeine is believed to be safe in moderate amounts, some health experts suggest that 300mg of caffeine ( the amount in about three cups of coffee) is a moderate intake. The amount of caffeine in a cup of coffee varies according to coffee bean, brewing technique, filter, etc. A random sample of eight ounce cups of coffee was obtained and the caffeine content(in milligrams) was measured. The data are given in the following table
71
75
88
89
89
90
93
95
96
97
100
101
106
107
109
112
115
115
a. Find the mean, median, variance, and standard deviation
b. Construct a modified box plot for these data
c. Use your results from part a and b to describe the data
d. Based on your results from parts a and b, do you beleive a person who drinks three cups of coffee ingests a moderate amount of caffeine? Justify your answer
My answers:
a. Mean = 99.11, Median = 96.50, Variance = 156.58, Standard Deviation = 12.51
b. Q1 = 89.00, Q3 = 107.50, Lowest Number = 71, Highest Number = 115, Median = 96.50
c. I have no clue in answering this question
d. I have no clue in answering this question
Explanation / Answer
1.
a. 7 paintings can be shoen from 20 stored paintings in
20C7 ways
=77520 ways
b. This is chosen by choosing all 7 from the 10 paintings of local artist
=10C7/20C7 = .0015
c.This is a perumation problem as order of painting displayed matters
So, 7*6*5*4*3*2*1 = 7! ways is the no. of ways to do it.
2.
All answers are right.Will solve c. Part as you have a problem here, your concepts of probability are right though :)
c."Justify tyour answer" from the probability you get. so, if probability of none of the College of Sc. ad tech ' books are choosen is too low then it means things weren't done randomly. If things were choosen randomly, then there is a very small(15C7/25C7 = .0134) change of not selecting Sc./Tech College' books.
3.
c. I have no clue in answering this question
Mean is more than median. --> This means that the distribution is slighly right skewed or positively skewed.
If you were to draw this distribution then you will see that the distibution is not symmtrical.
d. I have no clue in answering this question
The 3 cups of coffee is a moderate intake of 300mg. 1 cup is therefore 100gm. In our data the mean/median intake per cup is given i.e It is 99mg/cup. which is almost equal to the mean intake of caffeine per cup as suggested by health experts. Hence, I beleive a person who drinks three cups of coffee ingests moderate intake of caffine from the data provided to us.
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