Math 150
Review Test II
1.- If the random variable X has the following distribution: P (X = x) =
x
15
x = 1, 2, 3, 4, 5.
(a) Find E(X) = µ and σ
(b) Find P (X > 1|X ≤ 4)
2.- Suppose Shaq is a 55 % free throw shooter. If he shoots 20 free throws.
(a) What is the probability that he makes 12 shoots?
(b) How many shoots do you expected him to make?
(c) Use the normal distribution to approximate the probability in part (a).
3.- Suppose that the amount of caffeine in energy drinks is normally distributed, with a mean of
100mg. If 3%of the drinks have more than 145mg, what is the the standard deviation of this
distribution?
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4.- Suppose that the speed of cars in the freeway 405 is normally distributed with a mean speed
of 65 mph and a standard deviation of 8 mph. What is the probability that
(a) A randomly chosen car will travel faster than 85 mph?
(b) Now suppose that you pick a sample of 16 cars, what is the probability that the sample mean
will exceed 70 mph? Does CLT applies? explain?
5.- For the following data 10,11,4,8,15, and 7
(a) Find x and s.
(b) Construct a 95 percent C.I. for the above data.
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6.- A poll is conducted to see what proportion of people believe in Santa Claus. Out of 200 people
115 said that they believe in Santa claus.
(a) Find a 99% C.I for p.
(b) How large of a sample is needed to have an error of 2 %?
7.- A sample of 100 people was conducted to see how many cups of coffee (per day) people buy in
star-bucks. The sample have a mean of 4 and a standard deviation of 2.5. Find a 95 percent
C.I. for the true mean µ
8.- T/F section.
(a) You can always approximate the binomial distribution using the Normal distribution.
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(b) For any random variable X the variance is np(1-p).
(c) P (Z > a) = 1 − P (Z < a))
(d) Every random variable X has a probability distribution P (X = k)
(e) A binomial random variable with p = 0.4 and n = 20 has a mean of 8.
(f) P (Z > −1) = P (Z < 1)
(g) Zα/2 > Zα .
(h) x̄ is normally distributed even if the sample size is less than 30?
(i) For any normal random variable X, P (X > k) = P (Z >
4
k−µ
)
σ