Franchise Business Review stated over 50% of all food franchises earn a profit of less than $50,000 a year. In a sample of 130 casual dining restaurants, 81 earned a profit of less than $50,000 last year. Based upon a 95% confidence interval with a desired margin of error of .04, determine a sample size for restaurants that earn less than $50,000 last year.

We need a sample size of 564.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

For this problem, we have that:

The margin of error is:

95% confidence level

So , z is the value of Z that has a pvalue of , so .

Based upon a 95% confidence interval with a desired margin of error of .04, determine a sample size for restaurants that earn less than $50,000 last year.

We need a sample size of n

n is found when

So

Rounding up

We need a sample size of 564.

The sample size for restaurants that earn less than $50,000 last year is; 564

The formula for margin of error of proportions is; E = z√(p^(1 - p^)/n)

Where;

z is the critical value at given confidence level.

From tables, the value of z at confidence level of 95% is 1.96.

Now, we are given;

Margin of error; E = 0.04

Sample proportion; p^ = 81/130 = 0.6231

To determine a sample size for restaurants that earn less than $50,000 last year, we just make sample size (n) the subject of the formula in the formula for margin of error to get and then solve with the relevant values.

Thus;

n = z²(p^(1 - p^)/E²

Plugging in the relevant values gives;

n = 1.96²(0.6231(1 - 0.6231))/0.04²

n = 563.866

n ≈ 564

Read more about margin of error for proportions at; link

A) to solve for r, divide both sides by t.

R = d/t

B) divide total feet swam by time:

665,280 feet / 3 hours = 221,760 feet per hour

C) 1 mile = 5,280 feet. Divide feet per hour by 5280:

221,760/5280 = 42 miles per hour

D) long distances are usually calculated in miles because it’s smaller numbers which are easier to use in calculations.