Question

Solve what is asked in each of the points. It is important that you show your entire procedure to reach the result. 1. Mattel Corporation produces remote-controlled cars that run on AA batteries. The mean battery life for this product is 35.0 hours. The distribution of battery lives approximates a normal probability distribution with a standard deviation of 5.5 hours. As part of its program, Sony tests samples of 25 batteries. a) What can be said about the shape of the sampling distribution of the mean? b) What is the standard error of the sampling distribution of the mean? c) What proportion of the samples will have a mean shelf life of more than 36 hours? d) What proportion of the sample will have a mean shelf life greater than 34.5 hours? e) What proportion of the sample will have a mean shelf life between 34.5 and 36 hours? 2. The mean amount of groceries purchased by each customer at Churchill Grocery Store is $23.50, with a standard deviation of $5.00. Assume that the distribution of quantities purchased follows the normal distribution. For a sample of 50 customers, answer the following questions. a) What is the probability that the sample mean is at least $25.00? b) What is the probability that the sample mean is greater than $22.50 and less than $25.00? c) Within what limits will 90% of the sample means be presented? 3. Over the past decade, the average number of Information Systems Security Association members who experienced denial-of-service attacks each year was 510, with a standard deviation of 14.28 attacks. Assume nothing changes in this environment. a) What is the probability that this group will suffer an average of more than 600 attacks over the next 10 years? b) Calculate the probability that they will experience an average of 500 to 600 attacks over the next 10 years. c) What is the probability that they will experience an average of fewer than 500 attacks over the next 10 years? 4. Marty Rowatti has just taken over as director of the YMCA of South Jersey. He would like recent data on how long his current members have been members of the YMCA. To investigate this, suppose he selects a random sample of 40 current members. The mean membership length of those in the sample is 8.32 years, and the standard deviation is 3.07 years. a) What is the population mean? b) Construct a 90% confidence interval for the population mean. c) The previous director, in her brief report on her retirement, indicated that the average membership period was now “almost 10 years.” Does the information confirm this assertion? Please provide evidence. 5. A recent study by the American Automobile Dealers Association found that the mean amount of profit per car sold in a sample of 20 dealerships was $290, with a standard deviation of $125. Construct a 95% confidence interval for the population mean. 6. A survey of 36 randomly selected iPhone owners showed that the purchase price has a mean of $416, with a sample standard deviation of $180. a) Calculate the standard error of the sample mean. b) Calculate the 95% confidence interval of the mean. c) What size should the sample be to estimate the population mean within $10?

271

likes
1353 views

Answer to a math question Solve what is asked in each of the points. It is important that you show your entire procedure to reach the result. 1. Mattel Corporation produces remote-controlled cars that run on AA batteries. The mean battery life for this product is 35.0 hours. The distribution of battery lives approximates a normal probability distribution with a standard deviation of 5.5 hours. As part of its program, Sony tests samples of 25 batteries. a) What can be said about the shape of the sampling distribution of the mean? b) What is the standard error of the sampling distribution of the mean? c) What proportion of the samples will have a mean shelf life of more than 36 hours? d) What proportion of the sample will have a mean shelf life greater than 34.5 hours? e) What proportion of the sample will have a mean shelf life between 34.5 and 36 hours? 2. The mean amount of groceries purchased by each customer at Churchill Grocery Store is $23.50, with a standard deviation of $5.00. Assume that the distribution of quantities purchased follows the normal distribution. For a sample of 50 customers, answer the following questions. a) What is the probability that the sample mean is at least $25.00? b) What is the probability that the sample mean is greater than $22.50 and less than $25.00? c) Within what limits will 90% of the sample means be presented? 3. Over the past decade, the average number of Information Systems Security Association members who experienced denial-of-service attacks each year was 510, with a standard deviation of 14.28 attacks. Assume nothing changes in this environment. a) What is the probability that this group will suffer an average of more than 600 attacks over the next 10 years? b) Calculate the probability that they will experience an average of 500 to 600 attacks over the next 10 years. c) What is the probability that they will experience an average of fewer than 500 attacks over the next 10 years? 4. Marty Rowatti has just taken over as director of the YMCA of South Jersey. He would like recent data on how long his current members have been members of the YMCA. To investigate this, suppose he selects a random sample of 40 current members. The mean membership length of those in the sample is 8.32 years, and the standard deviation is 3.07 years. a) What is the population mean? b) Construct a 90% confidence interval for the population mean. c) The previous director, in her brief report on her retirement, indicated that the average membership period was now “almost 10 years.” Does the information confirm this assertion? Please provide evidence. 5. A recent study by the American Automobile Dealers Association found that the mean amount of profit per car sold in a sample of 20 dealerships was $290, with a standard deviation of $125. Construct a 95% confidence interval for the population mean. 6. A survey of 36 randomly selected iPhone owners showed that the purchase price has a mean of $416, with a sample standard deviation of $180. a) Calculate the standard error of the sample mean. b) Calculate the 95% confidence interval of the mean. c) What size should the sample be to estimate the population mean within $10?

Expert avatar
Birdie
4.5
103 Answers
(1) (a) aproximadamente normal

Frequently asked questions (FAQs)
What is the sum of the interior angles of a hexagon?
+
What is the maximum distance a particle can travel from its initial position if its motion is described by the equation y = 5sin(3x) over the interval 0 ≤ x ≤ π/3?
+
What is the inverse of the function f(x) = 1/x?
+
New questions in Mathematics
2x-y=5 x-y=4
3(4×-1)-2(×+3)=7(×-1)+2
If f(x) = 3x 2, what is the value of x so that f(x) = 11?
what is the annual rate on ​$525 at 0.046​% per day for 3 months?
9b^2-6b-5
2.3/-71.32
A construction company is working on two projects: house construction and building construction. Each house requires 4 weeks of work and produces a profit of $50,000. Each building requires 8 weeks of work and produces a profit of $100,000. The company has a total of 24 work weeks available. Furthermore, it is known that at least 2 houses and at least 1 building must be built to meet the demand. The company wants to maximize its profits and needs to determine how many houses and buildings it should build to meet demand and maximize profits, given time and demand constraints.
According to a survey in a country 27% of adults do not own a credit card suppose a simple random sample of 800 adults is obtained . Describe the sampling distribution of P hat , the sample proportion of adults who do not own a credit card
solve for x 50x+ 120 (176-x)= 17340
The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. 84. Find the probability that the average price for 30 gas stations is less than $4.55. a 0.6554 b 0.3446 c 0.0142 d 0.9858 e 0
In the telephone exchange of a certain university, calls come in at a rate of 5 every 2 minutes. Assuming a Poisson distribution, the average number of calls per second is: a) 1/8 b) 1/12 c) 1/10 d) 2/5 e) 1/24
A circular window has a rubber molding around the edge. If the window has a radius of 250 mm, how long is the piece of molding that is required ? (To the nearest mm)
0.1x8.2
If the regression equation is given by 4x –y + 5 = 0, then the slope of regression line of y on x is
Determine a general formula​ (or formulas) for the solution to the following equation.​ Then, determine the specific solutions​ (if any) on the interval [0,2π). cos30=0
Determine the Linear function whose graph passes through the points (6, -2) and has slope 3.
5a-3.(a-7)=-3
2p-6=8+5(p+9)
Mark is gluing a ribbon around the sides of a picture frame. The frame is 11 inches long and 7 includes wide. How much ribbon does Mark need?
x(squared) -8x=0