# CUNY Bronx Community College Binomial Distributions Questions

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I HAVE 15 BINOMIAL DISTRIBUTIONS QUESTIONS THAT I NEED HELP WITH. I DONT NEED THE PROCESS JUST THE ANSWERS. IT NEEDS TO BE THE EXACT ANSWERS IF NOT THE SYSTEM WONT ACCEPT IT.

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HOMEWORK 13 PART B
1.
A basketball player makes 75 % of the free throws he shoots. If he tries 8 free throws what is the
probability that:
(a) He will make exactly 2 throws?
(b) He will make exactly 5 throws?
(c) He will make either 2 or 5 throws?
2.
A surgery has a success rate of 75%. Suppose that the surgery is performed on three patients.
a.
What is the probability that the surgery is successful on at least 2 patients?
%
b. On average, how many surgeries can we expect to be successful if performed on a group of three
patients?
c.
What is the standard deviation of the number of successful surgeries performed on a group of
three patients?

3.
A basketball player makes 70% of the free throws he shoots. Suppose that he tries 15 free throws.
a.
What is the probability that he will make more than 7 throws?
%
b. How many baskets can the player expect to make if he takes 15 shots?
c.
What is the standard deviation of the number of successful free throws out of 15 total?

4.
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of
Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test
is conducted by randomly selecting
Southwest flights and observing whether they arrive on time.
(a) Find the probability that at least
flights arrive late .
(b) Would it be unusual for Southwest to have
(Enter YES or NO)
flights arrive late?
5.
It is estimated that 75% of a grapefruit crop is good; the other 25% have rotten centers that cannot be
detected until the grapefruit are cut open. The grapefruit are sold in sacks of 10.
a.
What is the probability of getting at least 9 good grapefruit in a sack?
%
b. If you purchase a sack of 10 grapefruit, how many can you expect to be good?
c.
What is the standard deviation of the number of good grapefruit in a sack of 10?

6.
Joe is new to cooking. The probability that Joe burns dinner is
.
(a) What is the probability that in the next
of them will burn? Express your
dinners Joe prepares,
answer as a decimal rounded to 4 decimal places after the decimal point.
(b) What is the probability that in the next
dinners Joe prepares, at least
of them will burn? Express
your answer as a decimal rounded to 4 decimal places after the decimal point.
(c) What is the probability that in the next
dinners Joe prepares, less than
of them will burn? Express
your answer as a decimal rounded to 4 decimal places after the decimal point.
7.
Suppose that
find
is a random variable with a binomial distribution. If
and
,
8.
Suppose that a variable has a binomial distribution with
of the variable?
= 12 and
= 0.01. What is the expected value
= 20 and
= 0.57.
Expected value =
9.
Suppose that a variable has a binomial distribution with
(a) What is the expected value of the variable?
Expected value =
(b) What is the standard deviation of the variable?
Standard deviation =
10.
A quiz consists of 10 multiple-choice questions, each with 4 possible answers but only one is correct. For
someone who makes random guesses for all of the answers, find the probability of passing if the minimum
11.
It is known that a certain hockey goalie will successfully make a save 86.03% of the time. Suppose that the
hockey goalie attempts to make 11 saves. What is the probability that the hockey goalie will make at least
8 saves?
Let
be the random variable which denotes the number of saves that are made by the hockey goalie.
Find the expected value and standard deviation of the random variable.
12.
If
is a binomial random variable, compute
for each of the following cases:
(a)
(b)
(c)
(d)
13.
If is a binomial random variable, compute the mean, the standard deviation, and the variance for each
of the following cases:
(a)
(b)
(c)
(d)
14.
Antibiotic for blood infections. Enterococci are bacteria that cause blood infections in hospitalized
patients. One antibiotic used to battle enterococci is vancomycin. A study by a large nationwide health
system revealed that % of all enterococci in its hospitals were resistant to vancomycin. Consider a
random sample of four patients with blood infections caused by the enterococci bacterium. Suppose that
all four patients are treated with the antibiotic vancomycin.
Note: Give your answers in decimal form with at least four decimal places.
a) What is the probability that all four patients are treated successfully?
b) What is the probability that the bacteria resist the antibiotic in at least one patient?
Note: A study by the Centers for Disease Control and Prevention on this subject was published in the New
York Times, Sept. 12, 1995.
15.
Consider an experiment in which
identical small boxes are placed side by side on a table. A crystal is
placed at random inside one of the boxes. A self-professed “psychic” is asked to pick the box that contains
the crystal.
a) If the psychic simply guesses, what is the probability that he/she picks the box with the crystal?
b) If the experiment is repeated
once?
times, what is the probability that psychic guesses correctly at least

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