Evaluate the expression. 4×6

According to the National Institute of Allergy and Infectious Diseases, 6% of American adults have a food allergy. A large compa

Vinil7 [7]

Answer:

a) The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

b) The expected value is 30 and the standard deviation is 5.31.

c) Close to 0% probability that none of the 500 employees has a food allergy

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have food allergy, or they do not. The probability of an adult having allergy is independent of other adults. So we use the binomial probability distribution 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.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

6% of American adults have a food allergy

This means that $p = 0.06$

500 employees.

This means that $n = 500$

(a) What are the assumptions/requirements of a Binomial distribution? Does this situation meet all these requirements?

The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

(b) What are the expected value and standard deviation of X (i.e., of the population)?

$E(X) = np = 500*0.06 = 30$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.06*0.94} = 5.31$

The expected value is 30 and the standard deviation is 5.31.

(c) What is the probability that none of the 500 employees has a food allergy?

This is P(X = 0).

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

$P(X = 0) = C_{500,0}.(0.06)^{0}.(0.94)^{500} \cong 0$

Close to 0% probability that none of the 500 employees has a food allergy

4 0

3 years ago

I had $13.00. My mom gave $10.00 my dad gave $30. My Aunt, My uncle and grandma gave me $100. I had another $7.00. How much did

Rina8888 [55]

$160 (if uncle, granny, aunt, gave $100 in total) $260 if they gave $100 each

8 0

3 years ago

Read 2 more answers

Plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz answer it

snow_tiger [21]

Answer:

each package will contain 2 toothbrushes and 3 bars of soap

Step-by-step explanation:

divide the number of each product by 12(number of packages)

24/12=2

36/12=3

7 0

2 years ago

Read 2 more answers

How old do you think people have to be to vote in the US? Should non-citizens be allowed to vote? Explain i need 6 sentence.

Alex73 [517]

Answer: To vote in the US you must be a US citizen, and you must be 18 and you must meet your state's residency and registration requirements. No, I do not think non-citizens should be allowed to vote. The reason I think non-citizens shouldn't be allowed to vote is because they are not an inhabitant. They also aren't national of a particular country or town. Therefore, they shouldn't be a part of the voting.

Hope that helps :/

6 0

2 years ago

This is due tomorrow, so please help and show step by step

Softa [21]

Answer:

slope = 3/2
y-intercept = 3
x-intercept = -2

Step-by-step explanation:

The slope is the coefficient of x when the equation is of the form ...

y = (something).

Here, we can put the equation in that form by subtracting 12x and dividing by the coefficient of y:

12x -8y = -24 . . . . . given

-8y = -12x -24 . . . . .subtract 12x

y = 3/2x +3 . . . . . . . divide by -8

This is the "slope-intercept" form of the equation. Generically, it is written ...

y = mx + b . . . . . . where m is the slope and b is the y-intercept

So, the above equation answers two of your questions:

slope = 3/2

y-intercept = 3

__

The x-intercept is found fairly easily from the original equation by setting y=0:

12x = -24

x = -24/12 = -2 . . . . . the x-intercept

_____

A graph of the equation can also show you these things. The graph shows a rise of 3 units for a run of 2, so the slope is rise/run = 3/2. The line crosses the axes at x=-2 and y=3, the intercepts.

8 0

3 years ago

Evaluate the expression. 4×6 – 21 ÷3​

Evaluate the expression. 4×6 – 21 ÷3