Download Quiz 3 Math 220 1. Foreign language study. Choose a student in

Quiz 3 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. Four candidates are seeking a vacancy on a school board. If A is twice as
likely to be elected as B, and B and C are given about the same chance of being
elected, while C is twice as likely to be elected as D, what are the probabilities
that
a) C will win;
b) A will not win?
Let P (D) = a, then P (B) = P (C) = 2a, P (A) = 4a,
and a + 2a + 2a + 4a = 1, a = 1/9.
so P (C) = 2/9, P (notA) = 1 − P (A) = 5/9.
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 x̄ 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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