Question

In: Statistics and Probability

Use the following information to answer questions 1-3. A population of 1,000 students spends an average...

Use the following information to answer questions 1-3.

A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken.

Determine the expected value of the sample mean.

	a.	$3.00
	b.	$10.50
	c.	$5.25

Determine the standard deviation of the sample mean.

	a.	0.363
	b.	3.000
	c.	0.375

Determine the probability that these 64 students will spend a combined total of more than $716.80.

	a.	0.973
	b.	0.027
	c.	0.062

Expert Solution

Let X be a random variable representing the expenditure. Then the population mean is E(X)= =10.5

and the population standard deviation is sample size is n=64

sample mean = where are samples.

the expected value of the sample mean=

the standard deviation of the sample mean=

because

So,

Standard deviation =

the probability that these 64 students will spend a combined total of more than $716.80

=

here as the sample size is greater than 30 so we use normal approximation to find the probability.

Z is a standard normal random variable.

the answer does not match any given option. So I think you can take 0.027 as the answer which is close to 0.031

orchestra answered 2 years ago

A population of 1,000 students spends an average of $10.50 a day on dinner.

A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? Explain the reason. Which theorem ensures the shape of the sampling distribution? b. What is the probability that these 64 students will spend a combined total of more than $715.21? c....

2. A population of 1,000 students spends an average of $10.50 a day on dinner. The...

2. A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? b. Confirm that the Central Limit Theorem condition(s) have been met and draw the sampling distribution c. What is the probability that these 64 students will spend a combined total...

A population of 1,000 students spends an average of $10.50 a day on dinner. The standard...

A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? b. What is the probability that these 64 students will spend an average of more than $11 per person? c. What is the probability that these 64 students will spend an...

The population of all Harvard students spends an average of $330 per semester on books. The...

The population of all Harvard students spends an average of $330 per semester on books. The population standard deviation of this expenditure is $65. A simple random sample of 40 students who attend the college is taken. a. Provide the sampling distribution for the sample mean. Can you assume a normal distribution for the sample mean? Why or why not? b. Calculate the probability that the average expenditure for the 40 students in the sample is between $320 and $350....

1. Answer the following finance questions, a. If you lend $1,000 to a friend for 3...

1. Answer the following finance questions, a. If you lend $1,000 to a friend for 3 years at an interest rate of 3%, how much will she owe you as balloon payment at the end? This is a balloon loan with all payment at the end of the loan's term. Round to the nearest cent. b. If you borrow $8,000 for 6 years at an interest rate of 6%, what are the annual payments you'd have to make to pay...

Use the following information to answer Questions 6 and 7. The 1-, 2-, 3-, and 4-year...

Use the following information to answer Questions 6 and 7. The 1-, 2-, 3-, and 4-year oil forward prices are $60, $58.35, $57.40, and $55 per barrel, respectively. Your firm is thinking about starting up an offshore drilling station and needs to forecast revenue over the next 4 years. Assume the risk-free rate is 5.25% each year and initial costs are $150,000,000. 6. (1 point) If your firm expects to extract 1,100,000 barrels of oil per year and each barrel...

Use the following information to answer questions 1 and 2. This is the shareholders’...

Use the following information to answer questions 1 and 2. This is the shareholders’ equity of Pinnacle on Dec 31, 2016. Common share (200,000 issued and outstanding) $ 800,000 7 percent, preferred shares (20,000 authorized, 18,000 issued) 200,000 Retained earnings 650,000 Total $ 1,650,000 Notes: Preferred shares were issued on Jan 1, 2013. No dividends declared or paid since 2013 until Pinnacle declared and paid $400,000 dividends on Dec 31, 2016. Assuming preferred shares...

Use the following information for questions 11-20: The average cholesterol level in the general US population...

Use the following information for questions 11-20: The average cholesterol level in the general US population is 189 mg/dL. A researcher wants to see if the average cholesterol for men in the US is different from 189 mg/dL. She takes a sample of 81 American males and finds a sample mean of 194 mg/dL and a sample standard deviation of 10.4. Create a 99.8% confidence interval for the true average cholesterol level of the general US male population. 11.What is...

Required information Use the following information to answer questions [The following information applies to the questions...

Required information Use the following information to answer questions [The following information applies to the questions displayed below.] The following information is available for Lock-Tite Company, which produces special-order security products and uses a job order costing system. April 30 May 31 Inventories Raw materials $ 31,000 $ 30,000 Work in process 9,500 18,200 Finished goods 54,000 34,000 Activities and information for May Raw materials purchases (paid with cash) 197,000 Factory payroll (paid with cash) 200,000 Factory overhead Indirect materials...

Use the information below for the following 3 questions A recent survey of 80 IU students...

Use the information below for the following 3 questions A recent survey of 80 IU students and 60 Ball State students found that the percent of IU students who are part of Greek life is 18%, while the percent Ball State students who are part of Greek life is 15%. Find the 95% confidence interval for the difference between the proportion of IU students who are part of Greek life compared to Ball State students, i.e. LaTeX: D=p_{IU}-p_{Ball\:State} D =...