Question

In: Statistics and Probability

1) An industry representative claims that 50 percent of all satellite dish owners subscribe to at...

1) An industry representative claims that 50 percent of all satellite dish owners subscribe to at least one premium movie channel. In an attempt to justify this claim, the representative will poll a randomly selected sample of dish owners.

a) The probability that none of the dish owners in the sample subscribes to at least one premium movie channel.

The correct answer is = P(X = 0) = 0.0625. But (4! 0!) is that not 6?

I went 4 X 3 X 2 X 1 / 4 X 0 X 0 X 0 = 24/4 = 6? Some one help please!

b) The probability that more than 2 dish owners in the sample subscribe to at least one premium movie channel.

The answer is 1 - [ 0.0625 + P(X=1) + P(X=2)] = 0.3125

I keep getting 0.0625. I went 1-[0.0625 + 0.5 + 0.375. Since P(X=1) = (8)(0.5)(0.125) = 0.5 and P(X=2) = (6(0.25)(0.25) = 0.375  Am i doing factorials wrong?

Solutions

Expert Solution

p: Probability that satellite dish owners subscribe to at least one premium movie channel = 50/100 =0.5

X : Number of dish owners in the sample subscribes to at least one premium movie channel.

n = 4

X follows Binomial distribution with n=4 and p =0.5

Probability mass function of X

probability that 'r' of the dish owners in the sample subscribes to at least one premium movie channel

a) The probability that none of the dish owners in the sample subscribes to at least one premium movie channel.

0! = 1

The probability that none of the dish owners in the sample subscribes to at least one premium movie channel = 0.0625

b) The probability that more than 2 dish owners in the sample subscribe to at least one premium movie channel = P(X>2)

P(X>2) = 1 - [P(X=0)+P(X=1)+P(X=2)]

From (a) P(X=0)=0.0625

P(X=0)+P(X=1)+P(X=2) = 0.0625+0.25+0.375 = 0.6875

P(X>2) = 1 - [P(X=0)+P(X=1)+P(X=2)] = 1 - 0.6875=0.3125

The probability that none of the dish owners in the sample subscribes to at least one premium movie channel = 0.3125

orchestra answered 2 years ago
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