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Binomial RV
Related Topics
Wize University Statistics Textbook > Discrete Probability Distributions
Binomial Distribution
8 Activities
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
)
.
a.
E
(
X
)
=
25
4
E(X)=\frac{25}{4}
E
(
X
)
=
4
25
and
σ
(
X
)
=
75
4
\sigma\left(X\right)=\frac{\sqrt{75}}{4}
σ
(
X
)
=
4
75
b.
E
(
X
)
=
75
4
E(X)=\frac{75}{4}
E
(
X
)
=
4
75
and
σ
(
X
)
=
75
4
\sigma\left(X\right)=\frac{\sqrt{75}}{4}
σ
(
X
)
=
4
75
c.
E
(
X
)
=
75
4
E(X)=\frac{75}{4}
E
(
X
)
=
4
75
and
σ
(
X
)
=
75
16
\sigma\left(X\right)=\frac{\sqrt{75}}{16}
σ
(
X
)
=
16
75
d.
E
(
X
)
=
25
3
E(X)=\frac{25}{3}
E
(
X
)
=
3
25
and
σ
(
X
)
=
75
3
\sigma\left(X\right)=\frac{\sqrt{75}}{3}
σ
(
X
)
=
3
75
e.
E
(
X
)
=
25
3
E(X)=\frac{25}{3}
E
(
X
)
=
3
25
and
σ
(
X
)
=
5
\sigma\left(X\right)=5
σ
(
X
)
=
5
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More Binomial Distribution Questions:
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 Distribution
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?
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
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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
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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).
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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
.