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4 years ago

Decide whether the Experiment is a Binomial Experiment. If it is not, explain why:

Mathematics

1 answer:

devlian [24]4 years ago

7 0

Answer:

Experiment 1 and 3 are clear binomial experiments.

Experiment 2 needs tweaking to be a binomial experiment.

Check Explanation.

Step-by-step explanation:

A binomial experiment is one in which

1) The probability of success doesn't change with every run or number of trials.

2) It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure.

3) The outcome of each trial/run of a binomial experiment is independent of one another.

Checking each of the experiments one at a time

- You observe the gender of the next 850 babies born at a local hospital. The random variable represents the number of boys.

For this experiment,

1) The probability of success doesn't change with every run or number of trials as it is a 50% chance that each child examined is a boy.

2) It consists of a fixed number of runs (850) with only two possible outcomes, success (if it's a boy) and failure (if it's a girl).

3) The probability of each trial being a boy is independent from all the other trials.

Hence, this experiment is a binomial experiment.

- You draw a marble 350 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.

For this experiment,

1) If the marbles aren't being replaced after each draw, the probability of success, that is, picking a particular marble colour changes from trial to trial.

2) Although, it consist of a fixed number of runs/trials, there are more than two possible outcomes with 3 types of colours. Unless the experiment focuses on one colour and treats the other two colours as 'others', this condition too isn't satisfied.

3) Without replacement, the probability of success (picking a particular marble colour) in one trial isn't independent of the other trials.

This is not a binomial experiment as it doesn't satisfy all the required conditions to be one.

- Testing a cough suppressant using 820 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.

1) The probability of success doesn't change with every run or number of trials as it is the same chance that each person finds the cough suppressant to be effective.

2) It consists of a fixed number of runs (820) with only two possible outcomes, success (cough suppressant is effective) and failure (cough suppressant isn't effective).

3) The probability of each trial being a person that finds the cough suppressant to be effective, is independent from all the other trials.

Hence, this experiment is a binomial experiment.

Hope this Helps!!!

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Milk is delivered to a chain of regional supermarkets once a week. If the weekly volume of sales in thousands of gallons is a ra

sleet_krkn [62]

Answer:

The chain of supermarkets must order 428.1 gallons of milk.

Step-by-step explanation:

Let's define the random variable X.

X : ''Weekly volume of sales in thousands of gallons''

X is a continuous random variable.

The probability density function for X is

$f(x)=7(1-x)^{6}$ when 0 < x < 1

$f(x)=0$ Otherwise.

Let's denote as ''a'' to the quantity of milk for the question.

We are looking for :

$P(X>a)=0.02$

$P(X>a)=\int\limits^1_a {f(x)} \, dx$

$P(X>a)=\int\limits^1_a {7(1-x)^{6}} \, dx$

$P(X>a)=(1-a)^{7}$

$(1-a)^{7}=0.02$

$a=1-\sqrt[7]{0.02}$

$a=0.4281$

a is in thousands of gallons, therefore the chain of supermarkets must order

428.1 gallons of milk in order to satisfy the question.

7 0

3 years ago

The total cost (in dollars) of producing x food processors is C(x) = 2500 + 50x -0.28.

Darya [45]

Answer:

The exact cost of producing the 21st food processor is $38.52.

The marginal cost to approximate the cost of producing the 21st food processor is $38.24

Step-by-step explanation:

Consider the provided function.

$C(x) = 2500 + 50x -0.28x^2$

(A) Find the exact cost of producing the 21st food processor

The exact cost producing 21st food processor is C(21)-C(20)

Substitute x=21 in above function.

$C(x) = 2500 + 50(21) -0.28(21)^2$

$C(x) = 2500 +1050 -123.48$

$C(x) = 3426.52$

Substitute x=20 in above function.

$C(x) = 2500 + 50(20) -0.28(20)^2$

$C(x) = 2500 +1000-112$

$C(x) = 3388$

The exact cost producing is:

$C(21)-C(20)=3426.52-3388=38.52$

Hence, the exact cost of producing the 21st food processor is $38.52.

Part (B) Use the marginal cost to approximate the cost of producing the 21st food processor,

To find the marginal cost first differentiate the function with respect to x.

$C(x) = 2500 + 50x -0.28x^2$

$C'(x) =50-0.56x$

Now substitute x=21 in above function.

$C'(x) =50-0.56(21)$

$C'(x) =50-11.76$

$C'(x) =38.24$

The marginal cost to approximate the cost of producing the 21st food processor is $38.24

5 0

3 years ago

Martina purchased a prepaid phone card for $20. long distance calls cost 13 cents a minute using this card. Martina used her car

Dima020 [189]

Phone card = $20
You need to minus 17.92 from 20 = $2.08
$2.08 / 0.13 = how many minutes
= 16

7 0

4 years ago

Read 2 more answers

Nevermind! Has been answered.

Paul [167]

Answer:

Ok that’s great.

6 0

4 years ago

A square has an area of 49 in.² what is each side of the perimeter

ludmilkaskok [199]

I hope this helps you

square one side a

Area=a.a

49=a.a

7.7=a.a

a=7

Perimeter=4a=4.7=28

8 0

3 years ago