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Nadusha1986 [10]
3 years ago
13

In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected for a

sample of 49 customers over a three-week period. If the sample provided a mean of $24.80 and the population standard deviation was known to be $5.
a) What is the 95% confidence interval for the population mean
b. Develop a 95% confidence interval estimate of the mean amount spent for dinner.Enter your answer using parentheses and a comma, in the form (n1,n2). Do not use dollar sign or spaces or include a comma in a number.
Mathematics
1 answer:
Softa [21]3 years ago
5 0

Answer:

95% Confidence interval = (23.4,26.2)

Step-by-step explanation:

In this problem we have to develop a 95% CI for the mean.

The sample size is n=49, the mean of the sample is M=24.8 and the standard deviation of the population is σ=5.

We know that for a 95% CI, the z-value is 1.96.

The CI is

M-z*\sigma/\sqrt{n}\leq\mu\leq M+z*\sigma/\sqrt{n}\\\\24.8-1.96*5/\sqrt{49}\leq\mu\leq 24.8+1.96*5/\sqrt{49}\\\\ 24.8-1.4\leq\mu\leq 24.8+1.4\\\\23.4\leq\mu\leq 26.2

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The length and width of the rectangular garden is estimated as-

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<h3>How to calculate perimeter of the rectangle?</h3>

A rectangle's perimeter is the total length and distance of its border across all sides. The perimeter of a rectangular box is a linear measurement that is expressed in meters, feet, cm, or yards. Let us first examine the two primary characteristics of a rectangle.

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The perimeter of the rectangle is given as-

Perimeter = 2(length + width)

perimeter= 256

Let the width of the rectangle be x.

Length is 8 feet longer than width, Thus,

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Substitute the values in the formula of perimeter;

256 = 2( x+ 8+ x)

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x=60

Thus, width = 60 ft.

Length = 60 + 8 = 68 ft.

Therefore, the length and width of the rectangular garden is estimated.

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brainly.com/question/2607596

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The complete question is -

A rectangular garden is fenced on all sides with 256 feet of fencing. The garden is 8feet longer than it is wide. Find the length and width of the garden.

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