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Nonamiya [84]
3 years ago
8

Can someone show me the steps to solving this?!?!!

Mathematics
1 answer:
Gala2k [10]3 years ago
6 0

Answer:

la raíz cuadrada entre 3

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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
kicyunya [14]

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.

8 0
3 years ago
Which relationship would most likely have a positive correlation?
tiny-mole [99]

Answer:

C.

Step-by-step explanation:

The only thing to do here is just check all of the answers.

A makes no sense, as the number of keys on a keyboard doesn't affect the amount of memory in a computer at all (no correlation).

B makes a bit more sense, but it's still wrong. If a train travels faster, it gets places quicker, or the time goes down. If (If one goes up, the other goes down) is true, then you have negative correlation.

C makes the most sense, as if there's more people at a game, then those more people will probably buy more hot dogs. If (If one goes up, so does the other) is true, then you have positive correlation, which is what we want.

4 0
2 years ago
Write and simplify an expression for the perimeter of each figure.
xxTIMURxx [149]
3a- 2b + 8b - 2 + 6a + 3c
3a + 6a -2b +8b + 3c - 2
9a + 6b + 3c - 2
4 0
3 years ago
How many 1/3s do you need to make 3/4
marin [14]

Answer:

2.25

Because I was asked this question and got it righg

5 0
2 years ago
Read 2 more answers
Face east, turn through an angle of 180 degree to your right, your final direction will be _________________. 
ANEK [815]

Answer:

West

10 cm

The first one

6 0
2 years ago
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