Question

The random variable *X* has a binomial distribution with
*n* = 10 and *p* = 0.04. Determine the following
probabilities.

Round your answers to six decimal places (e.g. 98.765432).

(a) P(X=5)=Enter your answer in accordance to the item a) of the question statement

(b) P(X≤2)=Enter your answer in accordance to the item b) of the question statement

(c) P(X≥9)=Enter your answer in accordance to the item c) of the question statement

(d) P(3≤X<5)=Enter your answer in accordance to the item d) of the question statement

Answer #1

Solution:

Using binomial probability formula ,

P(X = x) = (_{n} C _{x}) * p^{x} * (1 -
p)^{n - x} ; x = 0 ,1 , 2 , ....., n

Here , n = 10 , p = 0.04

1 - p = 1 - 0.04 = 0.96

a)

P(X = 5) = (_{10} C _{5}) * 0.04^{5} *
(0.96)^{10 - 5} = 0.000021

**P(X = 5) = 0.000021**

b)

P(X≤2)

= P(X = 0) + P(X = 1) + P(X = 2)

= (_{10} C_{0}) * 0.04^{0} *
(0.96)^{10 - 0} + (_{10} C
_{1}) * 0.04^{1} * (0.96)^{10 - 1}
+ (_{10} C _{2}) *
0.04^{2} * (0.96)^{10 - 2 }

=0.66483263599 + 0.27701359833 + 0.05194004969

= 0.993786

**P(X≤2) = 0.993786**

c)

P(X≥9)

= P(X = 9) + P(X = 10)

= 0.000000 + 0.000000

= 0.000000

**P(X≥9)= 0.000000**

d)

P(3≤X<5)

= P(X = 3) + P( X = 4)

= (_{10} C_{3}) * 0.04^{3} *
(0.96)^{10 - 3} + (_{10} C
_{4}) * 0.04^{4} * (0.96)^{10 - 4}

= 0.00577111663 + 0.00042081059

= 0.006192

**P(3≤X<5) = 0.006192**

The random variable X has a Binomial distribution with
parameters n = 9 and p = 0.7
Find these probabilities: (see Excel worksheet)
Round your answers to the nearest hundredth
P(X < 5)
P(X = 5)
P(X > 5)

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)

Suppose X is binomial random variable with n = 18 and p = 0.5.
Since np ≥ 5 and n(1−p) ≥ 5, please use binomial distribution to
find the exact probabilities and their normal approximations. In
case you don’t remember the formula, for a binomial random variable
X ∼ Binomial(n, p), P(X = x) = n! x!(n−x)!p x (1 − p) n−x . (a) P(X
= 14). (b) P(X ≥ 1).

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)

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 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 = 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)

x is a binomial random variable with n=10 and p=.5. find the
probability of obtaining from 6 to 9 tails of a fair coin. use the
binomial probability distribution formula

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)

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 27 minutes ago

asked 32 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago