Question

For each of the following binomial random variables, specify n and p. (a) A fair die is rolled 50 times. X = number of times a 5 is rolled. n = 50 Correct: Your answer is correct. p = 1/5 Incorrect: Your answer is incorrect. (b) A company puts a game card in each box of cereal and 1/100 of them are winners. You buy sixteen boxes of cereal, and X = number of times you win. n = 16 Correct: Your answer is correct. p = 1/100 Correct: Your answer is correct. (c) Jack likes to play computer solitaire and wins about 25% of the time. X = number of games he wins out of his next 26 games.μ =

Answer 1

Answer:

a) $n = 50, p = \frac{1}{6}$

b) $n = 16, p = \frac{1}{100}$

c) $n = 26, p = 0.25, \mu = 6.5$

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $p$ is the probability of X happening.

(a) A fair die is rolled 50 times. X = number of times a 5 is rolled

The die is rolled 50 times, so $n = 50$.

Each roll can have 6 outcomes. So the probability that 5 is rolled is $p = \frac{1}{6}$

(b) A company puts a game card in each box of cereal and 1/100 of them are winners. You buy sixteen boxes of cereal, and X = number of times you win.

You buy 16 boxes of cereal, so $n = 16$.

1 of 100 are winners. So $p = \frac{1}{100}$.

(c) Jack likes to play computer solitaire and wins about 25% of the time. X = number of games he wins out of his next 26 games.

He plays 26 games, so $n = 26$.

He wins 25% of the time, so $p = 0.25$

We have that $\mu = np$. So $\mu = 26*0.25 = 6.5$