Question

Please answer the three questions below:

1.)

Using the Binomial distribution,

If n = 8 and p = 0.5, then calculate the following

P(x < 3) =
	[three decimal accuracy]
P(x ≤ 3) =
	[three decimal accuracy]
P(x = 3) =
	[three decimal accuracy]
P(x ≥ 3) =
	[three decimal accuracy]
P(x > 3) =
	[three decimal accuracy]

2.)

A poll is given, showing 65% are in favor of a new building project.

If 8 people are chosen at random, what is the probability that exactly 5 of them favor the new building project?

3.)

A manufacturing machine has a 4% defect rate.

If 7 items are chosen at random, what is the probability that at least one will have a defect?

Answer 1

Solution:-

1)

n = 8, p = 0.50

a) P(x < 3) = 0.145

x = 3

By applying binomial distribution:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x < 3) = 0.1445

b) P(x < 3) = 0.363

x = 3

By applying binomial distribution:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x < 3) = 0.3633

c) P(x = 3) = 0.219

x = 3

By applying binomial distribution:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x = 3) = 0.2188

d) P(x > 3) = 0.856

x = 3

By applying binomial distribution:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x > 3) = 0.8555

e) P(x > 3) = 0.637

x = 3

By applying binomial distribution:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x > 3) = 0.6367