Question

In: Statistics and Probability

(A-Grade) The operations manager of a large production plant would like to estimate the mean amount...

(A-Grade) The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the population standard deviation of time for this assembly is 3.6 minutes.

1. After observing 120 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 92% confidence interval for the mean assembly time.

2. How many workers should be involved in this study in order to have the mean assembly time estimated up to 15 seconds with 92% confidence?

3. In a second study a sample 102 workers had standard deviation of 2.78 minutes, with 95% confidence level, construct a confidence interval for the population standard deviation.

Solutions

Expert Solution

1)

Given that,

Point estimate = sample mean = = 16.2

sample standard deviation = s = 3.6

sample size = n = 120

Degrees of freedom = df = n - 1 = 119

At 92% confidence level the t is ,

= 1 - 92% = 1 - 0.92 = 0.08

/ 2 = 0.08 / 2 = 0.04

t /2,df = t0.04,119 = 1.766

Margin of error = E = t/2,df * (s /n)

= 1.766* (3.6 / 119)

= 0.583

The 92% confidence interval estimate of the population mean is,

- E < < + E

16.2 - 0.583< < 16.2 + 0.583

15.617< < 16.783

( 15.617, 16.783)

2)

= 3.6 minutes = 3.6 * 60 = 216 seconds

Sample size = (Z/2 * / E)2

= (1.7507 * 216 / 15)2

= 636 (Rounded)

--------------------------------------

DEAR STUDENT,

IF YOU HAVE ANY QUERY ASK ME IN THE COMMENT BOX,I AM HERE TO HELPS YOU.PLEASE GIVE ME POSITIVE RATINGS

*****************THANK YOU***************


Related Solutions

The operations manager of a large production plant would like to estimate the mean amount of...
The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. After observing 135 workers assembling similar devices, the manager noticed that their average time was 16.0 minutes with a standard deviation of 3.7 minutes. Construct a 95% confidence interval for the mean assembly time. what is the margin of error of the confidence interval? new assume that the population standard deviation of assembly time...
The operations manager of a large production plant would like to estimate the mean amount of...
The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes. After observing 125 workers assembling similar devices, the manager noticed their average time was 16.2 minutes. Construct a 95% confidence interval for the mean assembly time.
The operations manager of a large production plant would like to estimate the mean amount of...
The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes. After observing 120 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 92% confidence interval for the mean assembly time. How many workers should be involved in this study in order to have the mean...
The operations manager of a large production plant would like to estimate the average amount of...
The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she estimates that the standard deviation is 0.25 hour. How large a sample of workers should she select if she wishes to estimate the mean assembly time to within 3.2 minutes at the 98% confidence level?
The operations manager of a large production plant would like to estimate the average amount of...
The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she guesses that the standard deviation is 10 minutes. How large a sample of workers should she take if she wishes to estimate the mean assembly time to within 20 seconds. Assume the confidence level to be 97%.
The manager of a door-making company would like to estimate the amount of time it takes...
The manager of a door-making company would like to estimate the amount of time it takes for a piece of wood to be moved, cut, and packaged at two different plants. At Plant A, the manager observed 21 pieces that processed with an average time of 14.2 minutes and standard deviation of 2.6 minutes. At the second plant, the manager observed 19 pieces with an average time of 13.1 minutes with a standard deviation of 1.9 minutes. a. Test whether...
5. After earning a loss of $6,000 from operations in 20Y5, the production manager would like...
5. After earning a loss of $6,000 from operations in 20Y5, the production manager would like to know the break- even point in sales dollars and units for the company. During 20Y5, the company sold 6,000 at $3 each. Variable costs for the year totaled $10,800. Determine the break-even point in dollars and units. 6. Would each of the following cause the break-even point to increase or decrease? a. Decrease in selling price of $5 per unit b. Decrease in...
You have been hired to be the operations/production manager for a plant that will manufacturer Nike’s...
You have been hired to be the operations/production manager for a plant that will manufacturer Nike’s Jordan line of sneakers. Describe in detail the strategic decisions you must make as it relates to successfully running this facility.
The plant manager at a company would like to perform an analysis for a new $125,000...
The plant manager at a company would like to perform an analysis for a new $125,000 machine. If she estimates benefits of $20,000 in the first year, and benefits are increasing by 10% per year a. What is the payback period for the machine? (Hint: The Payback Period is the length of time required to recover the initial cash outflows through the successive cash inflows, thus find the time when Cumulative PW (at 0%) becomes positive) b. Suppose that the...
The quality control manager of Ridell needs to estimate the mean breaking point of a large...
The quality control manager of Ridell needs to estimate the mean breaking point of a large shipment of helmets sent to the Philadelphia Eagles. Given the production process, the known standard deviation of the population of breaking points is 15.5 lbs. A random sample of 49 helmets were selected and subjected to increasing pressure until every one of them broke. The breaking point of each helmet was recorded, and average breaking point of the sample was 150 lbs. What are...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT