1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kompoz [17]
3 years ago
12

A popular resort hotel has 300 rooms and is usually fully booked. About 7% of the time a reservation is canceled before the 6:00

p.m. deadline with no pen-alty. What is the probability that at least 285 rooms will be occupied? Use the binomial distribution to find the exact valu
Mathematics
1 answer:
kicyunya [14]3 years ago
8 0

Answer:

8.69% probability that at least 285 rooms will be occupied.

Step-by-step explanation:

For each booked hotel room, there are only two possible outcomes. Either there is a cancelation, or there is not. So we use concepts of the binomial probability distribution to solve this question.

However, we are working with a big sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

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)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

A popular resort hotel has 300 rooms and is usually fully booked. This means that n = 300

About 7% of the time a reservation is canceled before the 6:00 p.m. deadline with no pen-alty. What is the probability that at least 285 rooms will be occupied?

Here a success is a reservation not being canceled. There is a 7% probability that a reservation is canceled, and a 100 - 7 = 93% probability that a reservation is not canceled, that is, a room is occupied.  So we use p = 0.93

Approximating the binomial to the normal.

E(X) = np = 300*0.93 = 279

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.93*0.07} = 4.42

The probability that at least 285 rooms will be occupied is 1 subtracted by the pvalue of Z when X = 285. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{285- 279}{4.42}

Z = 1.36

Z = 1.36 has a pvalue of 0.9131.

So there is a 1-0.9131 = 0.0869 = 8.69% probability that at least 285 rooms will be occupied.

You might be interested in
The bike path around the park near my house is 2/3 of a mile long. If I want to bike 10 miles, how many times would I have to bi
Olin [163]

Answer:

  15

Step-by-step explanation:

You want to find n such that ...

  n×(2/3 mi) = 10 mi

Divide by 2/3 mi:

  n = (10 mi)/(2/3 mi) = 10·3/2 = 15

You would have to bike the path 15 times to bike 10 miles.

4 0
3 years ago
Ill give brainly if right!!
S_A_V [24]

Answer:

The weight of square is 8 grams.

Step-by-step explanation:

Given that,

The weight of the circle = 2 grams

The weight of the triangle = 4 grams

We need to find the weight of the square. Let the weight of each square is w.

On LHS, 2 circles and 4 squares are there.

On RHS, 2 squares, 4 triangles and 2 circles are there.

For a balanced position,

Weight on LHS = Weight on RHS

2\times \text{weight of circle}+4\times \text{weight of squares}=2\times \text{weight of squares}+4\times \text{weight of triangles }+2\times \text{weight of circle}2(2)+4(w) = 2(w) + 4(4) +2(2)

4 + 4w = 2w +16 +4

4w-2w = 20-4

2w = 16

w = 8

So, weight of square is 8 grams.

4 0
2 years ago
4.
fenix001 [56]
The answer is C. because 3/16 is close to 3 because how it’s estimated of the germs and gasoline is how it’s going to hit africa and south america and dacota. hope this helps!!
5 0
2 years ago
Read 2 more answers
What’s the domain of (3,7),(4,1),(-1,-8),(2,2),(4,-1)
mafiozo [28]

Answer:

{-1,2,3,4}

Step-by-step explanation:

The domain is the input values

(3,7),(4,1),(-1,-8),(2,2),(4,-1)

(3,4,-1,2,4)

We do not list the repeats

(3,4,-1,2)

(-1,2,3,4)

6 0
3 years ago
9. Dagne measures and finds that she
Naddik [55]

Answer; 47.27 Inches

Let the height of Dagne be x.

Now we are told that she can do a vertical jump that is 27.5%  of her height. This is represented as 0.275x.

Now we are told the height she can jump is 13.2. Thus;

0.275x = 13.2

x = 13.2/0.275

x = 47.27 inches

7 0
2 years ago
Other questions:
  • 3,950 + 405<br>Enter your answer in the box<br>En ef answer​
    14·2 answers
  • Total departmental sales in the Housewares Department were $513000.00. A salesperson made 14% of the total departmental sales of
    9·1 answer
  • Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 mi
    8·1 answer
  • What is the exact value for the expression the square root of 56. − the square root of 14. + the square root of 126.? Simplify i
    7·1 answer
  • Eddie finds a good deal on a used car that he likes. He makes a down payment of $450 and pays $199 a month for 36 months. What i
    5·2 answers
  • In a sale, normal prices are reduced<br> by 25%.<br> The sale price of a calculator is<br> £8.82
    9·1 answer
  • Find the absolute maximum of m(t)=t^3-12t^2-144t and justify your answer​
    14·1 answer
  • A six-sided die is rolled 150 times.
    10·2 answers
  • What is the y- intercept of a line that goes through the points (3,-2)&amp; has a slope of -4?
    15·1 answer
  • Can somebody help me with the write
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!