A manager at a local manufacturing company has been monitoring the output of one of the...

A manager at a local manufacturing company has been monitoring the output of one of the machines used to manufacture chromium shells. Past data indicate that if the machine is functioning properly, the length of the shells produced by this machine can be modeled as being normally distributed with a mean of 118 centimeters and a standard deviation of 4.3 centimeters. Suppose 10 shells produced by this machine are randomly selected. What is the probability that the average length of these 10 shells will be between 116 and 120 centimeters when the machine is operating "properly?"

Solutions

Expert Solution

Given:

Given,

Mean, = 118

Standard deviation, = 4.3

n = 10

X ~ Normal (=118, ^2=4.3^2)

The probability that the average length of these 10 shells will be between 116 and 120 centimeters when the machine is operating properly :

P(116 < < 120) = P ((116-)//√n < (X-)//√n < (120-)//√n)

= P((116-118)/4.3/√10 < Z < (120-118)/4.3/√10)

= P(-1.47 < Z < 1.47)

= P(Z< 1.47) - P(Z< -1.47)

= 0.9292 - 0.0708

= 0.8584

The probability that the average length of these 10 shells will be between 116 and 120 centimeters when the machine is operating properly is 0.8584

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Susan is a cost accountant at a manufacturing company. She has been asked by her manager...

Susan is a cost accountant at a manufacturing company. She has been asked by her manager to update the cost for the company's lowest selling product, which is made at the plant where Susan is employed. He wants Susan to complete the task in one day, and does not want Susan to collect much information, because he does not anyone to know what Susan is doing. Susan believes the President of the company will use her numbers to justify closing...

You are the local emergency manager for a community that has been affected by a flood....

You are the local emergency manager for a community that has been affected by a flood. You now have to assess damages quickly. You have called a meeting of those who will assist. What steps do you take to ensure the safety of those involved in this function? What other things should you make them aware of? How will assessing damage caused by a flood any different than assessing damages from other types of hazards and disasters?

A Manufacturing group mass produces one product. It has 10 manufacturing locations and the manager of...

A Manufacturing group mass produces one product. It has 10 manufacturing locations and the manager of each location only reports the average quantity made per location each week. There are 9 production lines per location and each average reported is made up of one individual data point per production line. The Corporate Operations Manager claims to have made improvements that increased output. The historical corporate-wide output reported per line is 10,510 units with a standard deviation of 450 units. The...

is the new manager of the materials storeroom for Parr Manufacturing. Mary has been asked to...

is the new manager of the materials storeroom for Parr Manufacturing. Mary has been asked to estimate future monthly purchase costs for part #696, used in two of Parr's products. Mary has purchase cost and quantity data for the past 9 months as follows: Month Cost of Purchase Quantity Purchased January $12,675 2,720 parts February 12,110 2,820 March 17,426 4,095 April 15,825 3,724 May 13,025 2,912 June 14,022 3,321 July 15,290 3,688 August 10,094 2,262 September 14,970 3,552 Estimated monthly...

A chemical engineering has been working with a local manufacturing firm. For several years the firm...

A chemical engineering has been working with a local manufacturing firm. For several years the firm has been using chemical A as a solvent in their manufacturing process. Chemical A is carcinogenic, although studies supporting this claim have only recently been published. Without taking elaborate safety precautions, workers handling chemical A would be exposed to sufficient amounts to risk cancer. Moreover, the disease takes up to 20 years to manifest itself. The company has tried to implement safety procedures and...

You’ve been monitoring Bletchley Park Corporation and have calculated the following information. The company has a...

You’ve been monitoring Bletchley Park Corporation and have calculated the following information. The company has a debt to asset ratio of 57.45%, market beta of 1.26, unlevered beta of .82 (at a 40% marginal tax rate), and a cost of equity of 13.67%. The risk free rate is 1.8%. The risk premium due to financial risk is closest to?

8. You are the manager in charge of monitoring cash flow at a company that makes...

8. You are the manager in charge of monitoring cash flow at a company that makes photography equipment. Traditional photography equipment comprises 80 percent of your revenues, which grow about 2 percent annually. You recently received a preliminary report that suggests consumers take three times more digital photographs than photos with traditional film, and that the cross-price elasticity of demand between digital and disposable cameras is -0.2. In 2009, your company earned about $400 million from sales of digital cameras...

Kemboja Bhd, a local company which specializes in the manufacturing of surgical instruments, had recently been...

Kemboja Bhd, a local company which specializes in the manufacturing of surgical instruments, had recently been listed on the ACE Market of Bursa Malaysia. It has embarked on an aggressive strategy for expanding its activities into overseas market. Since a lot of cash is required to fund this ongoing venture, the company has decided not to pay any dividend to its shareholders. At least none are expected in the near future. The company is expected to earn RM2 million in...

1. You are a manager at a clothing manufacturing firm. One of your machines has just...

1. You are a manager at a clothing manufacturing firm. One of your machines has just broken down. You are trying to decide between the following two options. Compute the net present value of each to identify the best choice. Assume the interest rate is 5%. a. Pay $2000 to repair the machine. If you do this, the machine will produce 10,000 units this period and next period. Each unit sells for $50. b. Pay $5000 to buy a new,...

A manager of a company has been provided the following information on daily sales by the...

A manager of a company has been provided the following information on daily sales by the Economic Statistics division of the company. The population mean (µ) is $51,800 and the population standard deviation (σ) is $4000. The population has a normal distribution. a. Based on a random sample of 64 draw a diagram of the sampling distribution of x-bar . Be sure to label the axis and clearly explain the important features of the sampling distribution you have drawn. b....

Subjects