Assignement # 10
1)
A previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News. The factual data are compiled into Table 3.25.
Shirt#
≤ 210
211–250
251–290
290≤
1–33
21
5
0
0
34–66
6
18
7
4
66–99
6
12
22
5
Table 3.25
For the following, suppose that you randomly select one player from the 49ers or Cowboys. If having a shirt number from one to 33 and weighing at most 210 pounds were independent events, then what should be true about P(Shirt# 1–33|≤ 210 pounds)
2
The table shows the political party affiliation of each of 67 members of the US Senate in June 2012, and when they are up for reelection.
Up for reelection:
Democratic Party
Republican Party
Other
Total
November 2014
20
13
0
November 2016
10
24
0
Total
Table 3.20
What is the probability that a randomly selected senator is a Republican or is up for reelection in November 2014?
3
Carbon-14 is a radioactive element with a half-life of about 5,730 years. Carbon-14 is said to decay exponentially. The decay rate is 0.000121. We start with one gram of carbon-14. We are interested in the time (years) it takes to decay carbon-14 .
The distribution for X is…
4
According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between six and 15 pounds a month until they approach trim body weight. Let’s suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month.
a. Define the random variable. X =______
b. X ~______
c. Graph the probability distribution.
d. f(x) = ______
e. m =______
f. s =______
g. Find the probability that the individual lost more than ten pounds in a month.
h. Suppose it is known that the individual lost more than ten pounds in a month. Find the probability that he lost less than 12 pounds in the month.
i. P(7 < x < 13|x > 9) =______. State this in a probability question, similar to parts g and h, draw the picture, and find the probability.
