Crystal reads 25 pages in 1 hour. Write an equation to represent the 2

A quantity a varies directly as a quantity b, if, when b changes, a changes in the same ratio. What happens to the quantity a if

drek231 [11]

This means that if b doubles, then a will become half as large. For the inverse of the ratio 2 to 1 ("doubles") is the ratio 1 to 2 ("half"). The terms are exchanged; the inverse of the ratio a : b is the ratio b : a. When a varies inversely as b, we say that a is inversely proportional to b.

6 0

4 years ago

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

Use the symbols to right the expression and then evaluate it

EastWind [94]

Sixteen squared is written in maths as 16^2,
Four cubed is written in maths as 4^3

If you divide them you get 16^2/4^3
This is also written as (4^2)^2/4^3
4^4/4^3=
= 4^4-3=
= 4^1 =
= 4

4 0

3 years ago

Last summer, Troy Yaeger earned $2,855 . Troy is single and is not claimed as a dependent by anybody else. He will take the stan

butalik [34]

Answer: 8,545

Step-by-step explanation:

4 0

3 years ago

Please help me i'll count you as brainlist

kvv77 [185]

Answer:

b

Step-by-step explanation:

4 0

3 years ago

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