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Binomial Distribution
Related Topics
Wize University Statistics Textbook > Discrete Probability Distributions
Binomial Distribution
8 Activities
According to studies, 75% of rabbits like carrots. If 14 rabbits are selected at random, what is the probability that more than 8 but fewer than 11 of them like carrots?
(
14
9
)
(
0.75
)
9
(
0.25
)
5
(
14
10
)
(
0.75
)
10
(
0.25
)
4
{14\choose9}(0.75)^9(0.25)^5{14\choose10}(0.75)^{10}(0.25)^4
(
9
14
)
(
0.75
)
9
(
0.25
)
5
(
10
14
)
(
0.75
)
10
(
0.25
)
4
(
14
9
)
(
0.75
)
9
(
0.25
)
5
+
(
14
10
)
(
0.75
)
10
(
0.25
)
4
{14\choose9}(0.75)^9(0.25)^5+{14\choose10}(0.75)^{10}(0.25)^{4}
(
9
14
)
(
0.75
)
9
(
0.25
)
5
+
(
10
14
)
(
0.75
)
10
(
0.25
)
4
(
14
9
)
(
0.75
)
9
(
0.25
)
5
{14\choose9}(0.75)^9(0.25)^5
(
9
14
)
(
0.75
)
9
(
0.25
)
5
(
14
10
)
(
0.75
)
1
0
(
0.25
)
4
{14\choose10}(0.75)^10(0.25)^4
(
10
14
)
(
0.75
)
1
0
(
0.25
)
4
I don't know
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More Binomial Distribution Questions:
Binomial RV
A student randomly guesses on
25
M
C
25\ \ MC
25
M
C
questions, each with
4
4
4
options one of which is correct. Let
X
X
X
represent the number of correctly guessed answers. Determine the value of
E
(
X
)
E\left(X\right)
E
(
X
)
and
σ
(
𝑋
)
\sigma(𝑋)
σ
(
X
)
.
Binomial Distribution
A survey showed the following:
20% of students sleep under 4 hours a night
15% of students sleep between 4 and 5 hours a night
Binomial Distribution
According to a self-conducted study, 60% of the socks in your friend Nitsy’s top drawer have a hole in them. Given a random sample of 20 socks from Nitsy’s top drawer, what is the expected number of them which have holes?
Binomial RV
13 cards are drawn from a standard deck with replacement. Let X represent the number of aces drawn. Find the variance of X, that is
V
(
X
)
.
V(X).
V
(
X
)
.
Practice: Bernoulli Trials
When Ben asks a girl for her number, he gets it 20% of the time.
Binomial Distribution vs. Poisson Distribution vs. Hypergeometric Probability
Binomial [B], Poisson [P], or Hypergeometric [H]? Enter B, P, or H in the boxes below.
Binomial and Poisson Distributions
At a dangerous intersection, 2.5% of cars drive through a red light. Suppose 100 cars drove by.
Binomial Probability
Leo can shoot a bull’s eye 60% of the time. He has 10 bullets.
a) What’s the probability that he will shoot a bull’s eye exactly 8 of the 10 times?
b) What’s the probability that he will shoot a bull’s eye at most 8 times?
Binomial Distribution
The probability that Todd makes a sale is 40%. He engaged with 50 customers today.
What is the probability that exactly half of the customers will buy something from him today?
Statistical Properties: Practice
True or false? Enter "T" for true; "F" for false (without quotations).
Binomial distribution
Samuel plays a game in which he wins a prize 20% of the time.
Discrete Random Variable
An ordinary die is rolled 164 times. Determine the expected number of times the die shows a number greater than four.
Binomial Distribution
The binomial mean is 90 and the binomial standard deviation is 6. Find
n
n
n
.