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I’m working on a statistics test / quiz prep and need an explanation and answer to help me learn.

1. A class has 20 students. Twelve of the students are female, and eight are male. The teacher writes the
name of each student on a card. At the beginning of each class, the teacher shuffles the cards
thoroughly, chooses one at random, observes the name of the student, and replaces it in the set. In
the next class, the cards are thoroughly reshuffled, and the teacher again chooses a card at random,
observes the name, and replaces it in the set. The class meets a total of 26 times over the course of
the semester. Let Y be the number of cards observed with a name corresponding to a male student
during the semester.
(a) What is the distribution of Y?
(b) How many times (during the semester) do you expect the teacher to observe the card with a name
of a male student? What is the standard deviation of Y?
(c) What is the probability that the card with a name of a male student is observed more than half of
the time during the semester?
(d) What is the probability that Y is less than 9?
2. A small store keeps track of the number X of customers that make a purchase during the each hour
that the store is open. Based on the records, during an hour, 4 customers make a purchase 11% of the
time, 3 customers make a purchase 28% of the time, 2 customers make a purchase 31% of the time,
1 customer makes a purchase 17% of the time, and no customer makes a purchase 13% of the time.
(a) Graph the pmf and cdf of X.
(b) Determine the mean and standard deviation of X.
(c) Calculate the probability that no more than 2 customers make a purchase in an hour.
3. You collected the following sample of age and blood pressure from ten patients:
Patient
Blood Pressure
Age
67
1
118
2
54
105
3
66
120
71
132
5
38
98
6
59
140
7
62
143
8
68
138
9
80
142
10
74
125
For age only:
(a) What is the sample mean? What is the sample standard deviation? What is the sample median?
(b) Describe the distribution of the sample using the mean and median.
(c) What is the advantage of sample median over sample mean in measuring central tendency?
(d) Create a histogram of the sample.
For age and blood pressure:
(e) Create a scatterplot of age vs blood pressure.
(f) Describe the relationship between the two variables in terms of form, direction, and strength.
Measure the strength of the linear relationship between the two variables.
(g) Patients #6 and #7 were able to lower their blood pressures to 130 and 125, respectively, through
exercise and change in diet. Do the changes in blood pressures for the two patients make the
relationship between the two variables stronger or weaker? Explain.
4. Suppose the volume of juice being poured into containers in a filling operation is normally distributed
with a mean of m ounces and a standard deviation of 0.5 ounces. If the volume of juice in a container
is less than 15 ounces, the container gets discarded.
(a) If 9% of all containers are discarded, what is the mean m?
For parts (b)-(e), assume that the mean m is 16 ounces.
(b) What is the probability that a randomly selected container will be discarded?
(c) What is the probability that a randomly selected container will contain more than 16.5 ounces of
juice?
(d) What is the probability that the volume of juice in a randomly selected container is between 14.8
ounces and 15.7 ounces? Sketch the density curve of the purchase amounts, label u and u +
20, and shade the area under the density curve that esponds to the probability that the
volume of juice in a randomly selected container is between 14.8 ounces and 15.7 ounces.
(e) A container is randomly selected for inspection, and it was determined that the volume of juice
in the selected container was greater than 76.5% of all containers filled. What was the volume of
juice in the selected container?