Mathematics, 19.05.2020 02:07 Lena904

What is the probability that the proportion of people who will order coffee with their meal is between 2% of the population mean? If in a restaurant, the proportion of people who order coffee with their dinner is .9. A simple random sample of 144 patrons of the restaurant is taken.

Answers: 1

Show answers

Answers

Answer from: poop4992

57.62% probability that the proportion of people who will order coffee with their meal is within 2% of the population mean.

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 normally distributed samples are 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.

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, we have that $\mu = p, s = \sqrt{\frac{p(1-p)}{n}}$

In this question:

p = 0.9, n = 144

$\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{144}} = 0.025$

What is the probability that the proportion of people who will order coffee with their meal is within 2% of the population mean?

This is the pvalue of Z when X = 0.9 + 0.02 = 0.92 subtracted by the pvalue of Z when X = 0.9 - 0.02 = 0.88. So

X = 0.92

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

By the Central Limit Theorem

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

$Z = \frac{0.92 - 0.9}{0.025}$

Z = 0.8

Z = 0.8 has a pvalue of 0.7881

X = 0.88

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

$Z = \frac{0.88 - 0.9}{0.025}$

Z = -0.8

Z = -0.8 has a pvalue of 0.2119

0.7881 - 0.2119 = 0.5762

57.62% probability that the proportion of people who will order coffee with their meal is within 2% of the population mean.

Answer from: Quest

answer: x= -2y

step-by-step explanation:

Answer from: Quest

∞ this is your sign

Another question on Mathematics

Mathematics, 21.06.2019 15:40

What is the probability of rolling a single die greater than 4

Answers: 1

Answer

Mathematics, 21.06.2019 17:00

Simone claims the initial value and y-intercept are the same thing on a graph. is she correct? if you know that a line has a slope of and a y-intercept of 7, what is the equation for that line in slope-intercept form?

Answers: 1

Answer

Mathematics, 21.06.2019 17:00

You are on a cycling trip around europe with friends. you check the weather forecast for the first week. these are the temperatures for the week. sun mon tues wed thurs fri sat 16°c 20°c 24°c 28°c 28°c 23°c 15°c what is the mean temperature forecast for the week?

Answers: 1

Answer

Mathematics, 21.06.2019 17:20

Four airplanes carrying a total of 400 passengersarrive at the detroit airport. the airplanes carry, respectively,50, 80, 110, and 160 passengers.a) one of the 400 passengers is selected uniformly at random.let x denote the number of passengers that were on theairplane carrying the randomly selected passenger. find var(x)for x as given in the problemb) one of the 4 airplane drivers is also selected uniformly atrandom. let y denote the number of passengers on the chosen driver’s airplane. find var(y) for y as given in the problem

Answers: 3

Answer

You know the right answer?

What is the probability that the proportion of people who will order coffee with their meal is betwe...

Questions