Download Quiz 4 Math 220 1. Canada`s land area is 9,094,000 square

Quiz 4 Math 220
1. Canada’s land area is 9,094,000 square kilometers. Of this land, 4,176,000
square meters are forested. Choose a square kilometer of land in Canada at
random.
a). What the probability that the area you choose is forested?
P (forested)= 4176000
9094000 = 0.459
b). What is the probability that it is not forested?
P (not forested) = 1 -0.459= 0.541.
2. A loaded die means the 6 numbers do not come up equally likely. If
for a loaded die, the even numbers come up twice as likely as the odd numbers, what are the probabilities assigned to each of the six faces? i.e, get
P (1), P (2), · · · , P (6).
Let P (1) = P (3) = P (5) = a, then P (2) = P (4) = P (6) = 2a, since
the sum of the total probabilities is 1, we get 9a = 1, a = 1/9. That is,
P (1) = P (3) = P (5) = 1/9, P (2) = P (4) = P (6) = 2/9.
3. Heights of male college students have a normal distribution. Suppose
the mean height of all male college student is µ = 70 inches and the standard
deviation of the heights is σ = 2.8 inches.
Now you measure a random sample of 25 students. What is the probability
that the mean height of your sample is between 69 and 71 inches?
Note x̄ also follows a normal distribution with mean µx̄ = 70 and standard
= 0.56,
deviation σx̄ = √2.8
25
71−70
so P (69 ≤ x̄ ≤ 71) = P ( 69−70
0.56 ≤ z ≤ 0.56 ) = P (−1.79 ≤ z ≤ 1.79) =
0.9633 − 0.0367 = 0.9266.
The probability that the mean height of our sample is between 69 and 71
inches is 0.9266. This means if you take many, many samples of the same size
25, about 93% of the sample means fall between 69 and 71 inches.
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