STAT 3021 Minneapolis Community and Technical College Statistics Problems

HW 5STAT 3021
Q1. For each of these following examples, define the random variable of interest and recognize
their distributions respectively (one of the distributions learnt in class- Binomial, Multinomial,
Hypergeometric, Negative Binomial, Geometric, Poisson). Do not solve the problems in this part.
For example, you find a r.v. X given in the question follows a binomial distribution. Then you
need to specify the parameters B(n =?, p =?) according to our slides.
1. An oil company conducts a geological study that indicates that an exploratory oil well should
have a 20% chance of striking oil. What is the probability that the first strike comes on the
third well drilled?
2. Suppose you are given a 3 question multiple-choice test. Each question has 4 responses and
only one is correct. Suppose you want to find the probability that you can just guess at the
answers and get 2 questions right.
3. A crate contains 50 light bulbs of which 5 are defective and 45 are not. A Quality Control
Inspector randomly samples 4 bulbs without replacement. What is the probability that 4
bulbs are defective?
4. Let’s say that 80% of all business startups in the IT industry report that they generate a
profit in their first year. If a sample of 10 new IT business startups is selected, find the
probability that exactly seven will generate a profit in their first year.
5. Bob is a high school basketball player. He is a 70% free throw shooter. That means his
probability of making a free throw is 0.70. During the season, what is the probability that
Bob makes his third free throw on his fifth shot?
6. Your basketball team is playing a series of 5 games against your opponent. The winner is
those who wins more games (out of 5). Let assume that your team is much more skilled and
has 75% chances of winning. It means there is a 25% chance of losing. What is the probability
of your team gets 3 wins?
7. Births in a hospital occur randomly at an average rate of 1.8 births per hour. What is the
probability of observing 4 births in a given hour at the hospital?
8. Bob is a high school basketball player. He is a 70% free throw shooter. That means his
probability of making a free throw is 0.70. During the season, what is the probability that
Bob makes his first free throw on his fifth shot?
9. A box of candies has many different colors in it. There is a 15% chance of getting a pink
candy. What is the probability that exactly 4 candies in a box are pink out of 10?
10. A deck of cards contains 20 cards: 6 red cards and 14 black cards. 5 cards are drawn randomly
without replacement. What is the probability that exactly 4 red cards are drawn?
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STAT 3021
HW 5
11. In a certain town, 40% of the eligible voters prefer candidate A, 10% prefer candidate B, and
the remaining 50% have no preference. You randomly sample 10 eligible voters. What is the
probability that 4 will prefer candidate A, 1 will prefer candidate B, and the remaining 5 will
have no preference?
12. A small voting district has 101 female voters and 95 male voters. A random sample of 10
voters is drawn. What is the probability exactly 7 of the voters will be female?
13. Suppose you knew that the mean number of calls to a fire station on a weekday is 8. What
is the probability that on a given weekday there would be 11 calls?
14. An experiment of drawing a random card from an ordinary playing cards deck is done with
replacing it back. This was done ten times. Find the probability of getting 2 spades, 3
diamond, 3 club and 2 hearts.
15. It is known that 20% of products on a production line are defective. Products are inspected
until first defective is encountered. What is the probability that the first defective was found
after inspecting exactly 3 products?
16. A man was able to complete 3 files a day on an average. Find the probability that he can
complete 5 files the next day.
Q2. Answer the following questions from the book:
• Section 5.2(Binomial and multinomial): 5.4, 5.18, 5.79
• Section 5.3(Hypergeometric): 5.32, 5.40
• Section 5.4(Negative binomial and geometric): 5.90,5.91
• Section 5.5(Poisson): 5.58, 5.62, 5.68
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