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tia_tia [17]
3 years ago
12

The table shows distances run by Jeremy and Mateo in particular amounts of time.

Mathematics
1 answer:
saveliy_v [14]3 years ago
8 0

Answer:

Step-by-step explanation:

2/12 I think it's beenalong time  sinces have done this

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Ruby spends 1 1/4 hours a day practicing tye piano she practices 6 days a week how much time in all does ruby spend practicing t
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Which survey would you expect to have fair results regarding attitudes about carnivals?
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A film distribution manager calculates that 5% of the films released are flops. If the manager is right, what is the probability
erik [133]

Answer:

0.1357 = 13.57% probability that the proportion of flops in a sample of 572 released films would be greater than 6%

Step-by-step explanation:

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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}}

A film distribution manager calculates that 5% of the films released are flops.

This means that p = 0.05

Sample of 572

This means that n = 572

Mean and standard deviation:

\mu = p = 0.05

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.05*0.95}{572}} = 0.0091

What is the probability that the proportion of flops in a sample of 572 released films would be greater than 6%?

1 subtracted by the p-value of Z when X = 0.06. So

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

By the Central Limit Theorem

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

Z = \frac{0.06 - 0.05}{0.0091}

Z = 1.1

Z = 1.1 has a p-value of 0.8643

1 - 0.8643 = 0.1357

0.1357 = 13.57% probability that the proportion of flops in a sample of 572 released films would be greater than 6%

8 0
3 years ago
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