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Step2247 [10]
3 years ago
7

Your building plan for your restaurant includes one men's and women's restroom. The city inspector lets you kno that you must ha

ve at least 400 square feet per bathroom. If your building is a total 4,000 square feet, how many square feet are left for the development other nonbathroom areas?
Mathematics
1 answer:
Ivanshal [37]3 years ago
6 0

Answer: 3200 ft^2

Step-by-step explanation:

You have a total area of 4,000 ft^2.

In your plan, you will make two bathrooms (one men's restroom and one women's restroom)

We know that each one of them needs 400ft^2, then the total area needed is two times 400ft^2, or:

2*400ft^2 = 800ft^2

If we subtract this to the total area, we get:

4000ft^2 - 800ft^2 = 3200 ft^2

That is the square feet left for the development of other nonbathroom areas.

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Based on historical data, your manager believes that 41% of the company's orders come from first-time customers. A random sample
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Answer:

The probability that the sample proportion is between 0.35 and 0.5 is 0.7895

Step-by-step explanation:

To calculate the probability that the sample proportion is between 0.35 and 0.5 we need to know the z-scores of the sample proportions 0.35 and 0.5.

z-score of the sample proportion is calculated as

z=\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } } where

  • p(s) is the sample proportion of first time customers
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  • N is the sample size

For the sample proportion 0.35:

z(0.35)=\frac{0,35-0.41}{\sqrt{\frac{0.41*0.59}{72} } } ≈ -1.035

For the sample proportion 0.5:

z(0.5)=\frac{0,5-0.41}{\sqrt{\frac{0.41*0.59}{72} } } ≈ 1.553

The probabilities for z of being smaller than these z-scores are:

P(z<z(0.35))= 0.1503

P(z<z(0.5))= 0.9398

Then the probability that the sample proportion is between 0.35 and 0.5 is

P(z(0.35)<z<z(0.5))= 0.9398 - 0.1503 =0.7895

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