Question

In: Statistics and Probability

Question 1 “PhysicalFun” is a physical center which opens 24 hours per day. Each member of...

Question 1

“PhysicalFun” is a physical center which opens 24 hours per day. Each member of “PhysicalFun” has an access card. Members would be charged in a weekly basic (Sunday 12:00a.m. to Saturday 11: 59 p.m.) according to the accumulated number of hours of facilities used within a week. The weekly basic charge is $150 with an additional charge of $30 per hour. According to the company record, the number of hours a member spends in “PhysicalFun” in a week is normally distributed with mean 15 hours and standard deviation 2.8 hours.

(a) What are the average and standard deviation of weekly charge of a member?

(b) Suppose the middle 85% of weekly charge of a member is denoted by $(L1, L2). Find the values of L1 and L2.

(c) The senior management suggests fixing the weekly charge per member at $700. Assume the number of hours a member spends in “PhysicalFun” would not be changed due to the change of the weekly charge calculation method. What proportion of members would pay more money than the original system?

(d) How many hours does a member spend in “PhysicalFun” in a week so he / she would be beneficial by the new system?

Question 2

The Body Mass Index (BMI) is a value calculated based on the weight and the height of an individual. In a small European city, a survey was conducted one year ago to review the BMI of the citizens. In the sample with 200 citizens, the mean BMI was 23.3 kg/m2 and standard deviation was 1.5 kg/m2 . It is reasonable to assume the BMI distribution is a normal distribution.

(a) Find the point estimate of the population mean BMI one year ago

(b) Calculate the sampling error at 90% confidence.

(c) Construct a 90% confidence interval estimate of the population mean BMI one year ago.

This city launched a healthy exercise program to reduce citizen’s BMI after last year’s survey. Suppose the program effectively reduces the BMI of each citizen by 2.5%.

(d) Construct a 98% confidence interval estimate of the population mean BMI after the healthy exercise program. (Hint: find the updated sample mean and sample standard deviation of the BMI of the sample with 200 citizens selected last year)

Solutions

Expert Solution

Que.2

a. Sample mean is the point estimate of population mean. Therefore population mean is 23.3 kg/m2

b.

Sampling error at 90% confidence interval is,

c.

90% confidence interval one year ago is,

d.

98% confidence interval after healthy exercise program.

Each citizen's BMI is reduced by 2.5 %. Thus mean BMI become

23.3 - (23.3*2.5 / 100 ) = 22.72

We know that there is standard deviation is invariant to change of origin, hence standard deviation remains same.

Where is obtained using t table. It does not contain degrees of freedom 199, hence we use value for 200. Since sample size is very large both the values are approximately same.


Related Solutions

Question 1 “PhysicalFun” is a physical center which opens 24 hours per day. Each member of...
Question 1 “PhysicalFun” is a physical center which opens 24 hours per day. Each member of “PhysicalFun” has an access card. Members would be charged in a weekly basic (Sunday 12:00a.m. to Saturday 11: 59 p.m.) according to the accumulated number of hours of facilities used within a week. The weekly basic charge is $150 with an additional charge of $30 per hour. According to the company record, the number of hours a member spends in “PhysicalFun” in a week...
Question 1 “PhysicalFun” is a physical center which opens 24 hours per day. Each member of...
Question 1 “PhysicalFun” is a physical center which opens 24 hours per day. Each member of “PhysicalFun” has an access card. Members would be charged in a weekly basic (Sunday 12:00a.m. to Saturday 11: 59 p.m.) according to the accumulated number of hours of facilities used within a week. The weekly basic charge is $150 with an additional charge of $30 per hour. According to the company record, the number of hours a member spends in “PhysicalFun” in a week...
Consider a two person firm where each individual has total time = 24 hours per day...
Consider a two person firm where each individual has total time = 24 hours per day and a utility function U=5ln(x+1)+y. The team production function is such that each dollar of income generated by the firm requires two hour of effort per day as input. a) (8.5 marks) Derive the efficient level of effort for each partner, and the corresponding level of utility. b) (8.5 marks) Derive the equilibrium level of effort when each partner acts independently, taking as given...
QUESTION 1. The data for number of sleeping hours per day were recorded as below A...
QUESTION 1. The data for number of sleeping hours per day were recorded as below A sample of 15 males has a sample mean of 7.3 hours and the population standard deviation is assumed to be 1.26 hours. A sample of 18 females has a sample mean of 7.8 hours and the population standard deviation is assumed to be 1.51 hours. a) Use the P-VALUE METHOD with a 0.08 significance level to test the claim that the mean number of...
Consider an individual with total hours o t=24 per day. She is paid $10 per hour...
Consider an individual with total hours o t=24 per day. She is paid $10 per hour during the required 8 hours of working each day. She is also willing to work 2 extra hours per day, and gets paid $20 per hour for the overtime working. Explain the preferences of a worker and abusiness owner between overtime premium and straight-time equivalent. Your response should include a discussion of the income effect and the substitution efect.
A copy machine is available 24 hours a day. On a typical day, the machine produces...
A copy machine is available 24 hours a day. On a typical day, the machine produces 88 jobs. Each job takes about 3 minutes on the machine, 2 minutes of which is processing time and 1 minute is setup time (logging in, defining the job). About 23 Percent of the jobs need to be reworked, in which case the setup time and the processing time have to be repeated. The remainder of the time, the equipment is idle. What is...
6. The Glass House Restaurant is open 24 hours per day serving breakfast, lunch and dinner.  ...
6. The Glass House Restaurant is open 24 hours per day serving breakfast, lunch and dinner.   Fixed Costs are $42,000 per month. Variable Costs are $11.50 per meal.   The average total bill is $15 per customer. Ignore taxes and tips. Required: Compute the number of meals that must be served if Glass House Restaurant wishes to earn a profit of $9,000 Compute the Break Even point in Units Compute the Break Even point in Sales Dollars Assume that fixed costs...
A chemical industry produces 200 tons of sulfuric acid per day when running at 24 hours....
A chemical industry produces 200 tons of sulfuric acid per day when running at 24 hours. The acid is cooled in a counter flow double pipe heat exchanger from 60 0C to 40 0C. The cooling medium employed is water, which enters the heat exchanger at 15 0C and leaves at 20 0C. The acid flows through the inner pipe, while water flows through the annulus. The inner and outer diameters of the inner pipe are 70 mm and 80...
1) A manager wants to calculate the hours per patient day (HPPD) for a one day...
1) A manager wants to calculate the hours per patient day (HPPD) for a one day period. 96 hours were worked on the day shift 12 hour shift. 72 hours were worked on the night shift 12 hour shift. The midnight census was 21 patients. What was the HHPD for the 24 hour period? a) 7.0 HPPD b) 9.0 HPPD c) 5.5 HPPD d) 8.0 HPPD 2) You are the manager of an outpatient wellness clinic with a total fixed...
24 hours a day, there are workers who use 16 hours of leisure (L) and labor...
24 hours a day, there are workers who use 16 hours of leisure (L) and labor (E), excluding 8 hours of sleep. It benefits from the workers' leisure (L) and consumption (C). The utility function of this worker is U(L, C)=L*C. The worker's hourly wage is 10 and the given non-earned income is 10. When both labor and capital income are used for consumption (C), find consumption C that maximizes utility of workers. (However, the price of consumer goods is...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT