Question

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) |

Answer #1

Solution

Given that ,

p = 0.78

1 - p = 1 - 0.78 = 0.22

n = 15

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^{x} * (1 - p)^{n -
x}

a)

x = 14

P(X = 14) = ((15! / 14! (1)!) * 0.78^{14} *
(0.22)^{1}

= 0.1018

Probability = 0.1018

b)

x = 13

P(X = 13) = ((15! / 13! (2)!) * 0.78^{13} *
(0.22)^{2}

= 0.2010

Probability = 0.2010

b)

P(X 13) = P(X = 13) + P(X = 14) + P(X = 15)

= ((15! / 13! (2)!) * 0.78^{13} *
(0.22)^{2} + ((15! / 14! (1)!) * 0.78^{14} *
(0.22)^{1} + ((15! / 15! (0)!) * 0.78^{15} *
(0.22)^{0}

= 0.3269

Probability = 0.3269

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)

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)

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...

Assume that X is a Poisson random variable with
μ = 28. Calculate the following probabilities. (Do
not round intermediate calculations. Round your final answers to 4
decimal places.)
a.
P(X ≤ 16)
b.
P(X = 20)
c.
P(X > 23)
d.
P(25 ≤ X ≤ 34)

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)

Assume that X is a Poisson random variable with μ = 39. Use
Excel’s function options to find the following probabilities. (Do
not round intermediate calculations. Round your final answers to 4
decimal places.)
a.
P(X ≤ 34)
b.
P(X = 36)
c.
P(X > 39)
d.
P(38 ≤ X ≤ 43)

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