Quiz 4 Math 220
1. Foreign language study. Choose a student in grades 9 to 12 at random
and ask if she or he is studying a language other than English. Here is the
distribution of the results.
language
Spanish
probability 0.26
French
0.09
German
0.03
All others
0.03
None
0.59
a. What is the probability that a randomly chosen student is studying a
language other than English?
The probability is 1 − 0.59 = 0.41.
b. What is the probability that a randomly chosen student is studying
French, German or Spanish?
The probability is 0.26 + 0.09 + 0.03 = 0.38.
2. A loaded dice means the 6 numbers do not come up equally likely. If
for a loaded dice, the odd numbers comes up twice more likely than the even
numbers, what are the probabilities assigned to the six faces?
Let P (2) = P (4) = P (6) = a, then P (1) = P (3) = P (5) = 2a, since
the sum of the probabilities is 1, we get 9a = 1, a = 1/9. That is,
P (1) = P (3) = P (5) = 2/9, P (2) = P (4) = P (6) = 1/9.
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.
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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