# 1. In order to get more female customers, a new clothing store offers free gourmet coffee and pastry to its customers. The average daily revenue over the past five-week period has been $1,080 with a standard deviation of$260. Use this sample information to construct a 95% confidence interval for the average daily revenue. The store manager believes that the coffee and pastry strategy would lead to an average daily revenue of $1,200. Is the manager correct based on the 95% confidence interval? ## Answers Answer 1 Answer: Answer: No, the manager is not correct based on the 95% confidence interval. Step-by-step explanation: We are given that the average daily revenue over the past five-week period has been$1,080 with a standard deviation of $260, i.e.; X bar =$1080 and s = $260 and sample size, n = 35 . The Pivotal quantity for 95% confidence interval is given by; ~ where, X bar = sample mean =$1080

s  = sample standard deviation = $260 n = sample size = 35 {five-week} So, 95% confidence interval for average daily revenue, is given by; P(-2.032 < < 2.032) = 0.95 P(-2.032 < < 2.032) = 0.95 P(-2.032 * < < 2.032 * ) = 0.95 P(X bar - 2.032 * < < X bar + 2.032 * ) = 0.95 95% confidence interval for = [ X bar - 2.032 * , X bar + 2.032 * ] = [ 1080 - 2.032 * , 1080 + 2.032 * ] = [ 990.70 , 1169.30 ] No, the manager is not correct based on the fact that the coffee and pastry strategy would lead to an average daily revenue of$1,200 because the calculate 95% confidence interval does not include value of $1200. Therefore, the store manager believe is not correct. Answer 2 Answer: ### Final answer: The 95% confidence interval for the store's average daily revenue is calculated to be approximately ($993.97, $1166.03). Since$1200 is outside this interval, the manager's belief that the coffee and pastry strategy will lead to an average daily revenue of $1200 is not backed by this confidence level. ### Explanation: In the field of statistics, a confidence interval (CI) is a type of interval estimate that is used to indicate the reliability of an estimate. The method for calculating a 95% confidence interval for the average daily revenue involves the sample mean, the standard deviation, and the z-score associated with a 95% confidence level, which is approximately 1.96. Let's use the provided data to calculate: • Calculate the standard error by dividing the standard deviation by the square root of the sample size. Here, the standard deviation is$260, and the sample size is 5 weeks * 7 days/week = 35 days. So, the standard error is $260 / sqrt(35) =$43.89.
• Multiply the standard error by the z-score to get the margin of error. So, $43.89 * 1.96 =$86.03.
• Calculate the lower and upper bounds of the 95% confidence interval by subtracting and adding the margin of error from/to the sample mean. So, ($1080 -$86.03, $1080 +$86.03) = ($993.97,$1166.03).

The range of this 95% confidence interval is from $993.97 to$1166.03. This means we are 95% confident that the true average daily revenue lies within this interval. Since \$1200 lies outside this interval, the manager's belief is not supported by this confidence interval.

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## Related Questions

The Singh family ordered a large pizza with a diameter of 20 inches for dinner. If one of the members of the family ate one eighth of the pizza, how many square inches of pizza are remaining? Use 3.14 for π.274.75 square inches
39.25 square inches
314 square inches
157 square inches

274.75 square inches of pizza are remaining. Option A is the correct option.

What is π in math?

The ratio of a circle's diameter to its circumference, or "pi," is a mathematical constant that is roughly equal to 3.14159 (/pa/; also written as "pi"). Numerous mathematical and physics formulas contain the number. It is an irrational number, meaning that although fractions like 22/7 are frequently used to approximate it, it cannot be expressed exactly as a ratio of two integers.

Given that, the diameter of large pizza is 20 inches.

The radius of a circular shape is half of the diameter.

The radius of the pizza is (20 inches)/2 = 10 inches.

Area of a circular shape is ∏r² .

The area of the pizza is 3.14×10² = 314 in²

The total part of the pizza is considered as 1.

One-eighth of the pizza is eaten, and the remaining portion is (1-1/8) = 7/8.

The area of remaining pizza is

314 in²  × (7/8)

= 274.75 square inches

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Step-by-step explanation:

points are (-9,-8) and (-2,-8)

Pythagorean theorem can written as,

∴ d = 7 units

7 units

Step-by-step explanation:

Which type of angle is formed by sides of a square?

I believe it would be a right angle. Each corner of a square is a right angle.

A puppy weighs 12 ounces. What fractional part of a pound is this?

Hello,

Because 3 × 4 = 12

Hope this helps!!!! Happy Holidays!!!! (:

The puppy is 3/4 of a pound.

x = 115° , y = 140° , z = 40°

Step-by-step explanation:

40° , x and 25° lie on a straight line and sum to 180° , that is

x + 40° + 25° = 180°

x + 65° = 180° ( subtract 65° from both sides )

x = 115°

z and 40° are vertically opposite angles and are congruent , then

z = 40°

y and z lie on a straight line and sum to 180° , that is

y + 40° = 180° ( subtract 40° from both sides )

y = 140°

Help me out please need help !!

The answer is 1.25m + 3.50 = 12.35