Mathematics, 02.07.2020 20:01 adelawilliams60

A restaurant supply store surveys all chefs in the area and finds that 64 of the 85 head chefs in the area prefer their stores to the other restaurant supply store in town. To increase their sales, they are doing a statistical study of all chefs in the area. Use a calculator to find above what proportion will 80% of all sample proportions be in the sampling distribution of sample proportions of size 45.

Answers: 2

Show answers

Answers

Answer from: ballin3294

80% of all sample proportions in the sampling distribution of sample proportions of size 45 will be above 0.6988.

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 $s = \sqrt{\frac{p(1-p)}{n}}$

In this question:

$p = \frac{64}{85} = 0.7529, n = 45, \mu = 0.7529, s = \sqrt{\frac{0.7529*0.2471}{45}} = 0.0643$

Above what proportion will 80% of all sample proportions be in the sampling distribution of sample proportions of size 45.

Above the 100 - 80 = 20th percentile, which is X when Z has a pvalue of 0.2. So X when Z = -0.842.

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

By the Central Limit Theorem

$-0.842 = \frac{X - 0.7529}{0.0643}$

X - 0.7529 = -0.842*0.0643

X = 0.6988

80% of all sample proportions in the sampling distribution of sample proportions of size 45 will be above 0.6988.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

the functions have the same rate of change i think. i narrowed it down to this answer and "the rate of change of tour 1 is greater" but i got it wrong using that answer so im assuming its the answer above. (this is a question i also answered from the iready site if anyone needs a reference)

Another question on Mathematics

Mathematics, 21.06.2019 21:00

Hurrya vegetable garden and a surrounding path are shaped like a square that together are 11ft wide. the path is 2ft wide if one bag of gravel covers 9 square feet how many bags are needed to cover the path

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

40) linda was making chocolate truffles for the first day of school. the recipe for 20 chocolate truffles is: i cup of cream 2 cups of dark chocolate she noticed this will not be enough truffles for the 42 sure that all students in each homeroom next year. to be sure that all students receive a truffle, linda must adjust her recipe. a. complete the recipe for 42 truffles cups of cream - cups of dark chocolate work:

Answers: 2

Answer

Mathematics, 22.06.2019 02:30

Two farmers pay a total rent of $140 for a pasture. the first farmer placed $4 oxen in the pasture, and the second farmer placed $30 sheep in the pasture. the farmers split the rent based on the proportion of the pasture eaten by their own animals that month. how much should the first farmer pay, if 1 ox eats as much as 10 sheep in a month?

Answers: 1

Answer

Mathematics, 22.06.2019 05:00

Two trains leave a station on different tracks. the tracks make an angle of 130°, with the station as a vertex. the first train travels 100 km and makes its first stop at point a, while the second train travels 200 km and makes it first stop at point b. how far apart are the trains when both are at their first stop? round the answer to the nearest integer. a) 65 km b) 139 km c) 224 km d) 275 km

Answers: 2

Answer

You know the right answer?

A restaurant supply store surveys all chefs in the area and finds that 64 of the 85 head chefs in th...

Questions