In 2017, a website reported that only 10% of surplus food is being recovered in the food-service and restaurant sector, leaving approximately 1.5 billion meals per year uneaten. Assume this is the true population proportion and that you plan to take a sample survey of 575 companies in the food service and restaurant sector to further investigate their behavior.1. What is the probability that your survey will provide a sample proportion within ±0.03 of the population proportion? (Round your answer to four decimal places.)? 2. What is the probability that your survey will provide a sample proportion within ±0.015 of the population proportion? (Round your answer to four decimal places.)?

1. 0.9836 = 98.36% probability that your survey will provide a sample proportion within ±0.03 of the population proportion

2. 0.7698 = 76.98% probability that your survey will provide a sample proportion within ±0.015 of the population proportion.

Step-by-step explanation:

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

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 and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

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 and standard deviation

In this question, we have that:

So

1. What is the probability that your survey will provide a sample proportion within ±0.03 of the population proportion?

This is the pvalue of Z when X = 0.1 + 0.03 = 0.13 subtracted by the pvalue of Z when X = 0.1 - 0.03 = 0.07. So

X = 0.13

By the Central Limit Theorem

has a pvalue of 0.9918

X = 0.07

has a pvalue of 0.0082

0.9918 - 0.0082 = 0.9836

0.9836 = 98.36% probability that your survey will provide a sample proportion within ±0.03 of the population proportion.

2. What is the probability that your survey will provide a sample proportion within ±0.015 of the population proportion?

This is the pvalue of Z when X = 0.1 + 0.015 = 0.115 subtracted by the pvalue of Z when X = 0.1 - 0.015 = 0.085. So

X = 0.115

has a pvalue of 0.8849

X = 0.085

has a pvalue of 0.1151

0.8849 - 0.1151 = 0.7698

0.7698 = 76.98% probability that your survey will provide a sample proportion within ±0.015 of the population proportion.

the answer

b. they are parallel and will never intersect.

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: