Question

In: Economics

It is known that the duration of trouble-free operation of a new vacuum cleaner is normally...

It is known that the duration of trouble-free operation of a new vacuum cleaner is normally distributed with a standard deviation of 98 days. The research department randomly selects 25 customers who bought these vacuum cleaners and records the duration of trouble-free operation to construct a 95% confidence interval for population mean duration of trouble-free operation. The critical value needed is _________ a. 1.96 b. 1.645 c. 2.064 d. Insufficient information to compute the critical value

Solutions

Expert Solution

In the above question the confidence interval is clearly stated as 95% confidence interval. 95% confidence interval is commonly used reliability factor. 95% confidence interval means level of significance of 5%. That mean 2.5% on each tail.

Its given that distribution is normally distributed. So total area under the curve is 1. 2.5% = .025. i.e area under the shaded region is .025. Since the curve is symmetrical, the line middle of curve divide the curve into two parts of 0.5 area each.

Now consider the right side of the curve. shaded region is 0.025. So if we subtract 0.025 from from 0.5 we can find the area under the remaining area. i.e 0.475. Now look the z table for 0.475 and locate the corresponding z value, which would be 1.96.

Since the curve is symmetrical z values are same on both sides.

Therefore the critical values is a) 1.96


Related Solutions

You are about to launch a new Dyson Vacuum Cordless Cleaner Questions to be answered 1....
You are about to launch a new Dyson Vacuum Cordless Cleaner Questions to be answered 1. Describe the market research you would conduct to analyze and segment the market for the new vacuum cleaner. 2. Explain how you would select a target market or markets for the product offering. These can be domestic markets, international markets, or both. 3. In addition, explain the process of positioning the new Dyson vacuum cleaner relative to the competition. write a value proposition for...
Suppose that the duration of a particular type of criminal trial is known to be normally...
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 17 days and a standard deviation of 4 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places unless instructed otherwise. a. What is the distribution of X? X ~ N( , ) b. If one of the trials is randomly chosen, find the probability that it lasted at...
Suppose that the duration of a particular type of criminal trial is known to be normally...
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 17 days and a standard deviation of 6 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. If one of the trials is randomly chosen, find the probability that it lasted at least 13 days....
Suppose that the duration of a particular type of criminal trial is known to be normally...
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 17 days and a standard deviation of 6 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(___,___) b. If one of the trials is randomly chosen, find the probability that it lasted at least 15 days....
Describe the problem of the motor failure of the vacuum cleaner ? (Please write the answer...
Describe the problem of the motor failure of the vacuum cleaner ? (Please write the answer using the computer)
Describe the problems with the motor of the vacuum cleaner (Please write the answer using the...
Describe the problems with the motor of the vacuum cleaner (Please write the answer using the computer)
Explain the condition of the damaged motor of the vacuum cleaner (Please write the answer using...
Explain the condition of the damaged motor of the vacuum cleaner (Please write the answer using the computer)
A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current...
A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 9.2 A, while that of the vacuum cleaner is 5.9 A. Determine the power consumed by (a) the blow-dryer and (b) the vacuum cleaner. (c) Determine the ratio of the energy used by the blow-dryer in 18 minutes to the energy used by the vacuum cleaner in 56 minutes.
The Roomba by iRobot is a self-propelled vacuum cleaner that avoids falling off of stairs, vacuums...
The Roomba by iRobot is a self-propelled vacuum cleaner that avoids falling off of stairs, vacuums along walls and furniture, and recharges itself. Prices range from $150 - $399. If you were to buy this product, at what price point do you feel comfortable buying it online or in a retail store?
Vacuum cleaner companies often distribute advertisements that promote the amazing cleaning powers of their particular model...
Vacuum cleaner companies often distribute advertisements that promote the amazing cleaning powers of their particular model of vacuum cleaner. For example, some ads show vacuum cleaners picking up heavy objects such as nails, bolts, or ball bearings. However, an advertisement that each of us has received in the mail many times seems to top them all by showing that the compact version of a particular canister vacuum can pick up a 16-lb. bowling ball! We are not necessarily disputing this...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT