The amounts of time that customers stay in a certain restaurant for lunch is normally distributed with a standard deviation of 1
7 minutes. A random sample of 50 lunch customers was taken at this restaurant. Construct a 99% confidence interval for the true average amount of time customers spend in the restaurant for lunch. Round your answers to two decimal places and use ascending order.
2 answers:
Answer:
99% CI: [45.60; 58.00]min
Step-by-step explanation:
Hello!
Your study variable is:
X: Time a customer stays in a certain restaurant. (min)
X~N(μ; σ²)
The population standard distribution is σ= 17 min
Sample n= 50
Sample mean X[bar]= 51.8 min
Sample standard deviation S= 27.68
You are asked to construct a 99% Confidence Interval. Since the variable has a normal distribution and the population variance is known, the statistic to use is the standard normal Z. The formula to construct the interval is:
X[bar] ± *(σ/√n)
Upper level: 51.8 - 2.58*(17/√50) = 45.5972 ≅ 45.60 min
Lower level: 51.8 + 2.58*(17/√50) = 58.0027 ≅58.00 min
With a confidence level of 99%, you'd expect that the interval [45.60; 58.00]min will contain the true value of the average time customers spend in a certain restaurant.
I hope you have a SUPER day!
PS: Missing Data in the attached files.
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Law of Sines can help with this problem. Law of Sines can help find a missing angle or side if given two sides with respective opposite angles or two angles with respective sides. The formula for Law of Sines is sin(A)/a = sin(B)/b. A and B are the angles and a and b are the sides opposite the angles. Hopefully, the picture above helps you visualize everything.
Anyways, we know two sides and one angle, so Law of Sines is possible to use. The side opposite the right angle is 11. So, we have sin(90)/11. The other angle, we're looking for but we do know the side. The side opposite of angle M is 5. So, we have sin(M)/5. The Law of Sines formula tells us that Sin(A)/a = Sin(B)/b = Sin(C)/c but we don't need all the angles but just angle M. So we're going to just use Sin(A)/a = Sin(B)/b. We have already set up the equations so plug them in.
Sin(90)/11 = Sin(M)/5. Cross multiplication will get 5 × Sin(90) = Sin(M) × 11.
Sin(90) = 1. So, we get 1 × 5 and get after simplifying, 5 = Sin(M) × 11. We divide both sides by 11 to get Sin(M) by itself.
5/11 = Sin(M). Now we run into a problem. How do we get the angle M? We do the inverse sin or sin^-1 key if you're using a calculator. So, (5/11)sin^-1 = M. Our final answer is angle M = 27.03569... Hope this helped!
Side Notes: Make sure if you're using a calculator that you're in degrees and NOT radians unless the question calls for radians. Also, if you wanted to find all the angles of the triangle then once you find M, you could add that to the 90 degree angle and then subtract that from 180. You will find the other angle since you know two of them and there are only three of them that have to add to 180 degrees. I just like triangles, ;-) Good luck!
Anyways, we know two sides and one angle, so Law of Sines is possible to use. The side opposite the right angle is 11. So, we have sin(90)/11. The other angle, we're looking for but we do know the side. The side opposite of angle M is 5. So, we have sin(M)/5. The Law of Sines formula tells us that Sin(A)/a = Sin(B)/b = Sin(C)/c but we don't need all the angles but just angle M. So we're going to just use Sin(A)/a = Sin(B)/b. We have already set up the equations so plug them in.
Sin(90)/11 = Sin(M)/5. Cross multiplication will get 5 × Sin(90) = Sin(M) × 11.
Sin(90) = 1. So, we get 1 × 5 and get after simplifying, 5 = Sin(M) × 11. We divide both sides by 11 to get Sin(M) by itself.
5/11 = Sin(M). Now we run into a problem. How do we get the angle M? We do the inverse sin or sin^-1 key if you're using a calculator. So, (5/11)sin^-1 = M. Our final answer is angle M = 27.03569... Hope this helped!
Side Notes: Make sure if you're using a calculator that you're in degrees and NOT radians unless the question calls for radians. Also, if you wanted to find all the angles of the triangle then once you find M, you could add that to the 90 degree angle and then subtract that from 180. You will find the other angle since you know two of them and there are only three of them that have to add to 180 degrees. I just like triangles, ;-) Good luck!
Answer:
I got y as 30 degrees thanks have a nice day
