Which of the following is best used to measure the weight of a 18-wheeler truck

4. One in four people in the US owns individual stocks. You randomly select 12 people and ask them if they own individual stocks

BartSMP [9]

Answer:

a. The mean is 3, the variance is 2.25 and the standard deviation is 1.5.

b. 0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.

c. 0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.

d. 0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two

e. Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they own stocks, or they do not. The probability of a person owning stocks is independent of any other person, which means that the binomial probability distribution is used to solve this question.

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 combinations 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.

One in four people in the US owns individual stocks.

This means that $p = \frac{1}{4} = 0.25$

You randomly select 12 people and ask them if they own individual stocks.

This means that $n = 12$

a. Find the mean, variance, and standard deviation of the resulting probability distribution.

The mean of the binomial distribution is:

$E(X) = np$

So

$E(X) = 12(0.25) = 3$

The variance is:

$V(X) = np(1-p)$

So

$V(X) = 12(0.25)(0.75) = 2.25$

Standard deviation is the square root of the variance, so:

$\sqrt{V(X)} = \sqrt{2.25} = 1.5$

The mean is 3, the variance is 2.25 and the standard deviation is 1.5.

b. Find the probability that the number of people who own individual stocks is exactly six.

This is P(X = 6). So

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

$P(X = 6) = C_{12,6}.(0.25)^{6}.(0.75)^{6} = 0.0401$

0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.

c. Find probability that the number of people who say they own individual stocks is at least two.

This is:

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

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

$P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317$

$P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.0317 + 0.1267 = 0.1584$

0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.

d. Find the probability that the number of people who say they own individual stocks is at most two.

This is:

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

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

$P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317$

$P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267$

$P(X = 2) = C_{12,2}.(0.25)^{2}.(0.75)^{10} = 0.2323$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0317 + 0.1267 + 0.2323 = 0.3907$

0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two.

e. Are the events in part c. and in part d. mutually exclusive

Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.

5 0

3 years ago

Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she sold 6 fewer books

laila [671]

Let, the number of books on Monday = m
On Tuesday = 2m
On Wednesday = 2m - 6

Equation: m + 2m + (2m - 6) = 19
You can solve it:
5m = 19 + 6
m = 25/5
m = 5

In short, He sold 5 books on Monday

Hope this helps!

7 0

4 years ago

Which statement is equivalent to the inequality 5z < 30

solmaris [256]

For this question you should divide both sides of the equaltion by 5 so you ill have:
5z/5 < 30/5
z < 6 :)))
i hope this is helpful
have a nice day

6 0

4 years ago

Please & thankssssss

malfutka [58]

Multiply both sides of the equation by 28 4y+7=10
Then move constants to the right side and change its sign 4y=10-7
Now subtract the numbers 4y=3 divide both sides by 4 so your answer is y=3/4

8 0

3 years ago

Exponential form of 3a x 3a x 3a

Semmy [17]

Answer:

3a then the power of 3 thing i cannot do rn

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers