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suter [353]
3 years ago
9

Michelle built a fence around her square garden. If Michelle used 72 yards of fencing to enclose her garden, what is the length

of each side? 12 yards 16 yards 18 yards 36 yards
Mathematics
1 answer:
Ierofanga [76]3 years ago
4 0
The length of each side is 18 yards
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The equation shows that n - 2 (2 less than a number) and then = 6

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Water stations will be placed every 400 meters of a 5 - kilometer race. How many water stations are needed? (hint 1 kilo=1,000 m
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1 kilo=1000 meters. 
The race is 5,000 meters total.
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a) A large hotel in Miami has 900 rooms (all rooms are equivalent). During Christmas, the hotel is usually fully booked. However
Olegator [25]

Answer:

14.69% probability that this happens

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

1000 people were given assurance of a room.

This means that n = 1000

Let us assume that each customer cancels their reservation with a probability of 0.1.

So 0.9 probability that they still keep their booking, which means that p = 0.9

Probability more than 900 still keeps their booking:

n = 1000, p = 0.9

So

\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{1000}} = 0.0095

901/1000 = 0.91

So this is 1 subtracted by the pvalue of Z when X = 0.91.

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

By the Central Limit Theorem

Z = \frac{0.91 - 0.9}{0.0095}

Z = 1.05

Z = 1.05 has a pvalue of 0.8531

1 - 0.8531 = 0.1469

14.69% probability that this happens

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