Omar uses 1/6 of his tickets to ride the water slide. How many tickets does he use he has 24 in total?

Carson purchased supplies for his computer for $64. The sales tax was $4.16. He gave the salesperson $80. How much change did he

krek1111 [17]

To work this out you need to do 80 - 64 - 4.16 = 11.48

he received $11.48 change

3 0

3 years ago

four times the sum of some number plus 1 is equal 12 times the difference of the number and 3. Find the number

aleksklad [387]

<h3>The value of x is equal to 2.</h3>

4(x + 1) = 12(3 - x)

Distributive property on both sides.

4x + 4 = 36 - 12x

Add 12x to both sides.

16x + 4 = 36

Subtract both sides by 4.

16x = 32

Divide both sides by 16.

x = 2

5 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)?

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