Question

Let X represent a binomial random variable with n = 180 and p = 0.25. Find the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

a. P(X ≤ 45)

b. P(X = 35)

c. P(X > 55)

d P(X ≥ 50)

Answer #1

X represent a binomial random variable with n = 180 and p = 0.25

The probability mass function of X is given as -

We can use Normal Aprroximation to Binomial distribution. But here we will use direct Binomial distribution approach.

a.

**P(X ≤ 45) = 0.5399**

b.

**P(X=35) = 0.0157**

c.

**P(X>55)=0.0376**

d.

**P(X ≥ 50)=0.2176**

Let X represent a binomial random variable with
n = 180 and p = 0.25. Find the following
probabilities. (Do not round intermediate calculations. Round your
final answers to 4 decimal places.)
a. P(X ≤ 45)
b. P(X = 35)
c. P(X > 55)
d P(X ≥ 50)

Let X represent a binomial random variable with
n = 360 and p = 0.82. Find the following
probabilities. (Do not round intermediate calculations.
Round your final answers to 4 decimal places.
Probability
a.
P(X ≤ 290)
b.
P(X > 300)
c.
P(295 ≤ X ≤ 305)
d.
P(X = 280)

Let X represent a binomial random variable with n = 170 and p =
0.6. Find the following probabilities. (Do not round intermediate
calculations. Round your final answers to 4 decimal places.)
Probability
a.P(X ≤ 100)
b.P(X > 110)
c.P(105 ≤ X ≤ 115)
d.P(X = 90)

Assume that X is a binomial random variable with
n = 15 and p = 0.78. Calculate the following
probabilities. (Do not round intermediate calculations.
Round your final answers to 4 decimal places.)
Assume that X is a binomial random variable with
n = 15 and p = 0.78. Calculate the following
probabilities. (Do not round intermediate calculations.
Round your final answers to 4 decimal places.)
a.
P(X = 14)
b.
P(X = 13)
c.
P(X ≥ 13)

Assume that X is a binomial random variable with
n = 12 and p = 0.90. Calculate the following
probabilities. (Do not round intermediate calculations.
Round your final answers to 4 decimal places.
a.
P(X = 11)
b.
P(X = 10)
c.
P(X ≥ 10)

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)

Suppose that x is a binomial random variable with
n = 5, p = .56, and q = .44.
(b) For each value of x, calculate
p(x). (Round final
answers to 4 decimal places.)
p(0) =0.0164
p(1) =0.1049
p(2) =0.2671
p(3) =0.3399
p(4) =0.2163
p(5) =0.0550
(c) Find P(x = 3).
(Round final answer to 4 decimal
places.)
P(x = 3)
0.3399selected answer
correct
(d) Find P(x ≤ 3).
(Do not round intermediate calculations.
Round final answer to 4 decimal...

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)

Let X be a binomial random variable with n = 10 and p = 0.2.
Find the following values. (Round your answers to three decimal
places.) (a) P(X = 4) (b) P(X ≥ 4) (c) P(X > 4) (d) P(X ≤ 4) (e)
μ = np μ = 2.00 (correct) (f) σ = npq σ = 1.265 (correct)

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 =

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