Question

Find the mean and standard deviation for each binomial random
variable:

**a.** *n* = 40, ππ = .85 **(Round your
mean value to 2 decimal places and standard deviation to 4 decimal
places.)**

Mean | |

Standard deviation | |

**b.** *n* = 78, ππ = .65 **(Round your
mean value to 2 decimal places and standard deviation to 4 decimal
places.)**

Mean | |

Standard deviation | |

**c.** *n* = 30, ππ = .70 **(Round your
mean value to 2 decimal places and standard deviation to 4 decimal
places.)**

Mean | |

Standard deviation | |

Answer #1

Find the mean, μ, and standard deviation, σ, for a binomial
random variable X. (Round all answers for σ to three decimal
places.)
(a) n = 45, p = .50.
μ =
σ =
(b) n = 1, p = 0.25.
μ =
σ =
(c) n = 100, p = 0.75.
μ =
σ =
(d) n = 30, p = .01.
μ =
σ =

(i) A binomial random variable has a mean equal to 187 and a
standard deviation of 12.
(a) Find the value of n. (Give your answer correct to the
nearest whole number.)
(b) Find the value of p. (Give your answer correct to four
decimal places.)
(ii) he probability of success on a single trial of a binomial
experiment is known to be 0.3. The random variable x,
number of successes, has a mean of 75.
(a) Find the number...

If ? is a binomial random variable, compute the mean, the
standard deviation, and the variance for each of the following
cases:
(a) ?=5, ?=0.6
?=
?2=
?=
(b) ?=6, ?=0.3
?=
?2=
?=
(c) ?=4, ?=0.7
?=
?2=
?=
(d) ?=3, ?=0.6
?=
?2=
?=

If ? is a binomial random variable, compute the mean, the
standard deviation, and the variance for each of the following
cases:
(a) ?=4,?=0.8
?=
?2=
?=
(b) ?=5,?=0.3
?=
?2=
?=
(c) ?=6,?=0.9
?=
?2=
?=
(d) ?=5,?=0.9
?=
?2=
?=

1) Suppose a random variable, x, arises from a binomial
experiment. Suppose n = 6, and p = 0.11.
Write the probability distribution. Round to six decimal places,
if necessary.
x
P(x)
0
1
2
3
4
5
6
Find the mean.
μ =
Find the variance.
σ2 =
Find the standard deviation. Round to four decimal places, if
necessary.
σ =
2) Suppose a random variable, x, arises from a binomial
experiment. Suppose n = 10, and p =...

If x is a binomial random variable, compute the mean,
the standard deviation, and the variance for each of the following
cases:
(a)
n=4,p=0.7
μ=
σ2=
σ=
(b)
n=3,p=0.7
μ=
σ2=
σ=
(c)
n=5,p=0.4
μ=
σ2=
σ=
(d)
n=5,p=0.8
μ=
σ2=
σ=

Given independent random variables with means and standard
deviations as shown, find the mean and standard deviation of each
of these variables:
Mean
SD
a) 4X
b) 4Y+3
c) 2X+5Y
X
70
14
d) 5X−4Y
e) X1+X2
Y
10
5
a) Find the mean and standard deviation for the random variable
4X.
E(4X)=_____________
SD(4X)=_______________
(Round to two decimal places as needed.)
b) Find the mean and standard deviation for the random variable
4Y+3.
E(4Y+3)= ________________
SD(4Y+3)= _____________________
(Round to...

1) Let X be a binomial random variable with p = 0.55, and n= 40.
Find the probability
that X is more than 2 standard deviations from the mean of X.

Let X be a binomial random variable with n =
100 and p = 0.2. Find approximations to these
probabilities. (Round your answers to four decimal places.)
(c) P(18 < X < 30)
(d) P(X ≤ 30)

Let X be a binomial random variable with n =
8, p = 0.4. Find the following values. (Round your answers
to three decimal places.)
(a)
P(X = 4)
(b)
P(X ≤ 1)
(c)
P(X > 1)

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