Mathematics, 30.06.2021 19:50 dsporski

A film distribution manager calculates that 9% of the films released are flops. If the manager is right, what is the probability that the proportion of flops in a sample of 469 released films would be greater than 6%

Answers: 1

Show answers

Answers

Answer from: miklff

0.9884 = 98.84% probability that the proportion of flops in a sample of 469 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 9% of the films released are flops.

This means that p = 0.09

Sample of 469

This means that n = 469

Mean and standard deviation:

$\mu = p = 0.09$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{469}} = 0.0132$

What is the probability that the proportion of flops in a sample of 469 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

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

$Z = \frac{0.06 - 0.09}{0.0132}$

Z = -2.27

Z = -2.27 has a p-value of 0.0116

1 - 0.0116 = 0.9884

0.9884 = 98.84% probability that the proportion of flops in a sample of 469 released films would be greater than 6%.

Answer from: Quest

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (

Answer from: Quest

fwms@lil_ben06

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 19:00

Satchi found a used bookstore that sells pre-owned dvds and cds. dvds cost $9 each, and cds cost $7 each. satchi can spend no more than $45.

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

East black horse $0.25 total budget is $555 it'll cost $115 for other supplies about how many flyers do you think we can buy

Answers: 1

Answer

Mathematics, 21.06.2019 22:00

Nikita wants to apply for student aid to fund her college education. arrange the steps involved in nikita’s application for financial aid

Answers: 3

Answer

Mathematics, 21.06.2019 22:30

Tommy buys a sweater that is on sale for 40% off the original price. the expression p -0.4p can be used to find the sale price of the sweater, where p is the original price of the sweater. if the original price of the sweater is 50, what is the sale price?

Answers: 1

Answer

You know the right answer?

A film distribution manager calculates that 9% of the films released are flops. If the manager is ri...

Questions