Question

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=

?=

Answer #1

If ? is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases:

?= np

?2= npq

?=sqrt(npq)

q = 1 - p

(a) ?=4,?=0.8

?= 4*0.8 = 3.2

?2= 4*0.8*0.2 = 0.64

?= Sqrt(0.64) = 0.8

(b) ?=5,?=0.3

?= 5*0.3 = 1.5

?2= 5*0.3*0.7 = 1.05

?= sqrt(1.05) = 1.024695

(c) ?=6,?=0.9

?= 6*.9 = 5.4

?2= 6*.9*.1= 0.54

?= sqrt(0.54) = 0.734847

(d) ?=5,?=0.9

?= 5*0.9 = 4.5

?2= 5*0.9*0.1 = 0.45

?= sqrt(0.45) = 0.67082

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 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=

If ?x is a binomial random variable, compute ?(?) for each of
the following cases:
(a) ?(?≤6),?=8,?=0.2
?(?)=
(b) ?(?>4),?=5,?=0.5
?(?)=
(c) ?(?<2),?=3,?=0.8
?(?)=
(d) ?(?≥5),?=9,?=0.6
?(?)=

If x is a binomial random variable, compute P(x) for each of the
following cases:
(a) P(x≤4),n=6,p=0.9
P(x)=
(b) P(x>2),n=6,p=0.7
P(x)=
(c) P(x<2),n=3,p=0.1
P(x)=
(d) P(x≥1),n=7,p=0.3
P(x)=

If XX is a binomial random variable, compute the
probabilities for each of the following cases:
(a)
P(X≤1),n=9,p=0.3P(X≤1),n=9,p=0.3
Probability =
(b)
P(X>4),n=5,p=0.5P(X>4),n=5,p=0.5
Probability =
(c)
P(X<1),n=5,p=0.25P(X<1),n=5,p=0.25
Probability =
(d)
P(X≥3),n=6,p=0.25P(X≥3),n=6,p=0.25
Probability =

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...

Let
X have a normal distribution with mean 6 and standard deviation 3
1) Compute the probability that X>8.7 .
0-0.1
0.1-0.2
0.2-0.3
0.3-0.4
0.4-0.5
0.5-0.6
0.6-0.7
0.7-0.8
0.8-0.9
0.9-1
2) Compute the probability that X<0 .
0-0.1
0.1-0.2
0.2-0.3
0.3-0.4
0.4-0.5
0.5-0.6
0.6-0.7
0.7-0.8
0.8-0.9
0.9-1
3) Compute the probability that |X-6|>1.9 .
0-0.1
0.1-0.2
0.2-0.3
0.3-0.4
0.4-0.5
0.5-0.6
0.6-0.7
0.7-0.8
0.8-0.9
0.9-1

Find the mean, variance, and standard deviation of the random
variable having the probability distribution given in the following
table. (Round your answers to four decimal places.)
Random variable, x
-7
-6
-5
-4
-3
P(X = x)
0.13
0.16
0.4
0.15
0.16

(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 x is a binomial random variable, compute P(x) for each of the
following cases (record your answer to atleast 3 decimal
places):
(a) P(x≤1),n=3,p=0.5
P(x)=?
(b) P(x>4),n=8,p=0.6
P(x)= ?
(c) P(x<4),n=6,p=0.7
P(x)= ?
(d) P(x≥3),n=7,p=0.3
p(x)=?

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