Question

In: Statistics and Probability

A production line manager wants to determine how well the production line is running. He randomly...

A production line manager wants to determine how well the production line is running. He randomly selected 90 items off of the assembly line and found that 8 were defective. (Assume all conditions have been satisfied for building a confidence interval). Find the 99% confidence interval.

(0.0234, 0.1099)

(0.0116, 0.1662)

(0.0301, 0.1477)

(0.0396, 0.1382)

Solutions

Expert Solution

Solution :

Given that,

n = 90

x = 8

Point estimate = sample proportion = = x / n = 8/90=0.0889

1 -   = 1- 0.0889 =0.9111

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

  Margin of error = E = Z/2   * (((( * (1 - )) / n)

= 2.576* (((0.0889*0.9111) /90 )

E = 0.0773

A 99% confidence interval is ,

- E < p < + E

0.0889 - 0.0773  < p < 0.0889 +0.0773

0.0116 , 0.1662

(0.0116, 0.1662)

orchestra answered 2 years ago
Next > < Previous

Related Solutions

You are manager of a manufacturing business. Business is going very well and one production line...
You are manager of a manufacturing business. Business is going very well and one production line is at full capacity. You want to double the size of the production line. Engineering has estimated the cost and time required. It can be accomplished without effecting the existing production. The timing of the cash flows for the facility is as follows. Month Cash Flow 1 $       (20,000.00) 2 $       (45,000.00) 3 $       (55,000.00) 4 $       (70,000.00) 5 $       (75,000.00) 6 $       (80,000.00)...
A production line produces monitors, 7% of which have cosmetic defects. A quality manager randomly selects...
A production line produces monitors, 7% of which have cosmetic defects. A quality manager randomly selects 7 monitors from the production line and is interested in the number of defective parts found. For questions 2-9 compute the probability for the number of monitors that have a cosmetic defect. (Use 5 decimal places for your answers): Table 01 x f (x) 0 x0 1 x1 2 x2 3 x3 4 x4 5 x5 6 x6 7 x7 Compute the probability for...
A manager is trying to determine which of three production processes to implement to produce a component for a new product line.
A manager is trying to determine which of three production processes to implement to produce a component for a new product line. Process A would entail a variable cost of $17 per unit and an annual fixed cost of $150,000. Process B would entail a variable cost of $11 per unit and an annual fixed cost of $250,000. Process C would entail a variable cost of $20 per unit and an annual fixed cost of $180,000.a. Develop three separate models...
A manager is trying to determine which of three production processes to implement to produce a component for a new product line.
A manager is trying to determine which of three production processes to implement to produce a component for a new product line. Process A would entail a variable cost of $17 per unit and an annual fixed cost of $150,000. Process B would entail a variable cost of $11 per unit and an annual fixed cost of $250,000. Process C would entail a variable cost of $20 per unit and an annual fixed cost of $180,000.Develop three separate models in...
A manager is trying to determine which of three production processes to implement to produce a component for a new product line.
A manager is trying to determine which of three production processes to implement to produce a component for a new product line. Process A would entail a variable cost of $17 per unit and an annual fixed cost of $150,000. Process B would entail a variable cost of $11 per unit and an annual fixed cost of $250,000. Process C would entail a variable cost of $20 per unit and an annual fixed cost of $180,000.a. Develop three separate models...
One of Philip’s investments is going to mature, and he wants to determine how to invest...
One of Philip’s investments is going to mature, and he wants to determine how to invest the proceeds of $50,000. Philip is considering two new investments: a stock mutual fund and a one-year certificate of deposit (CD). The CD is guaranteed to pay a 3% return. Philip estimates the return on the stock mutual fund as 11%, 2%, or -9%, depending on whether market conditions are good, average, or poor, respectively. Philip estimates the probability of a good, average, and...
One of Mabel Smith’s investments is going to mature, and he wants to determine how to...
One of Mabel Smith’s investments is going to mature, and he wants to determine how to invest the proceeds of $30,000. Mabel is considering two new investments: a stock mutual fund and a one-year certificate of deposit (CD). The CD is guaranteed to pay an 8% return. Mabel estimates the return on the stock mutual fund as 16%, 9%, or 22%, depending on whether market conditions are good, average, or poor, respectively. Mabel estimates the probability of a good, average,...
It is known that 20% of products on a production line are defective. a. Randomly pick...
It is known that 20% of products on a production line are defective. a. Randomly pick 5 products. What is the probability that exactly 2 are defective? b. Products are inspected until first defective is encountered. Let X = number of inspections to obtain first defective. What is the probability that X=5?
(2)   The general manager of a regional airline wants to determine how effective their rebate promotions...
(2)   The general manager of a regional airline wants to determine how effective their rebate promotions are. In these campaigns, rebates are valid for one week. To examine their effectiveness, the executive records the daily ticket sales (in $100,000s) during the campaign and during the week after the campaign ends. Test the research hypothesis that sales increase during the campaign at the 5% significance level. a.      What are the null and alternative hypotheses? b.      What is the appropriate p-value? c.      ...
The manager of a lightbulb factory wants to determine if there is any difference in the...
The manager of a lightbulb factory wants to determine if there is any difference in the mean life expectancy of the bulbs manufactured on two different types of machines. A random sample of 4 lightbulbs from machine I indicates a sample mean of 352 hours and a sample standard deviation of 98 ​hours, and a similar sample of 4 lightbulbs from machine II indicates a sample mean of 364 hours and a sample standard deviation of 125 hours. Complete parts​...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT