Which of the expressions are equivalent to the one below? Check all that apply.

105. Suppose that the probability that an adult in America will watch the Super Bowl is 40%. Each person is considered independe

Ainat [17]

Answer:

a. X is the number of adults in America that need to be surveyed until finding the first one that will watch the Super Bowl.

b. X can take any integer that is greater than or equal to 1. $\rm X\in \mathbb{Z}^{+}$ .

c. $\rm X \sim NB(1, 0.40)$ .

d. $E(\rm X) = 2.5$ .

e. $P(\rm X = 7) = 0.0187$ .

f. $P(\text{X} = 3) +P(\text{X} = 4) = 0.230$ .

Step-by-step explanation:

In this setting, finding an adult in America that will watch the Super Bowl is a success. The question assumes that the chance of success is constant for each trial. The question is interested in the number of trials before the first success. Let X be the number of adults in America that needs to be surveyed until finding the first one who will watch the Super Bowl.

It takes at least one trial to find the first success. However, there's rare opportunity that it might take infinitely many trials. Thus, X may take any integer value that is greater than or equal to one. In other words, X can be any positive integer: $\rm X\in \mathbb{Z}^{+}$ .

There are two discrete distributions that may model X:

The geometric distribution. A geometric random variable measures the number of trials before the first success. This distribution takes only one parameter: the chance of success on each trial.
The negative binomial distribution. A negative binomial random variable measures the number of trials before the r-th success. This distribution takes two parameters: the number of successes $r$ and the chance of success on each trial $p$ .

$\rm NB(1, p)$ (note that $r=1$ ) is equivalent to $\sim Geo(p)$ . However, in this question the distribution of $\rm X$ takes two parameters, which implies that $\rm X$ shall follow the negative binomial distribution rather than the geometric distribution. The probability of success on each trial is $40\% = 0.40$ .

$\rm X\sim NB(1, 0.40)$ .

The expected value of a negative binomial random variable is equal to the number of required successes over the chance of success on each trial. In other words,

$\displaystyle E(\text{X}) = \frac{r}{p} = \frac{1}{0.40} = 2.5$ .

$P(\rm X = 7) = 0.0187$ .

Some calculators do not come with support for the negative binomial distribution. There's a walkaround for that as long as the calculator supports the binomial distribution. The r-th success occurs on the n-th trial translates to (r-1) successes on the first (n-1) trials, plus another success on the n-th trial. Find the chance of (r-1) successes in the first (n-1) trials and multiply that with the chance of success on the n-th trial.

$P(\text{X} = 3)+P(\text{X} = 4) = 0.230$ .

3 0

3 years ago

Janna has 34 pennies. Mandy has 48 pennies. Mandy says they have 72

krok68 [10]

Answer:

Mandy should add the tens before she adds the ones.

Step-by-step explanation:

There are no other good answers and the correct answer is 82 pennies.

3 0

3 years ago

Read 2 more answers

Help me plss I don't get it

olga55 [171]

15 games per month because all you had to do was divided 195 by 13 which equals 15 games per month

7 0

3 years ago

Which algebraic expression is a polynomial with a degree of 3?

KatRina [158]

It would be the second choice. This expression is a polynomial because it is multiple terms and is a degree of three because the largest exponent is three. So your answer is:
2y^3 + 5y^2 - 5y

7 0

3 years ago

Consider the original triangle and the enlargement,<br> 2 cm<br> 8 cm<br> 3 cm

AURORKA [14]

Answer: 12

Explaining: 2 times 4 is 8 so makes it reasonable to say 3 times 4 is 12. Also both of the triangles are similar just the left is smaller and the right is larger.

4 0

3 years ago