A three part Stats problem Help

[Dani16]

-I have no clue where to start-

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A roadway construction process uses a machine that pours concrete onto the roadway and measures the thinckness of the concrete so the roadway will measure up to the required depth in inches. The concrete thickness needs to be consistent across the road, but the machine isn't perfect and it is costly to operate. Since there's a safety hazard if the roadway is thinner than the minimum 23 inches thickness, the company sets the machine to average 26 inches for the batches of concrete. They believe the thickness level of the machine's concrete output can be decribed by a normal model with standard deviation 1.75 inches. [show work]

a) What percent of the concrete roadway is under the minimum depth ?


b) The company's lawyers insist that no more than 3% of the output be under the limit. Because of the expense of operating the machine, they cannot afford to reset the mean to a higher value. Instead they will try to reduce the standard deviation to achieve the "only 3% under" goal. What SD must they attain?


c) Explain what achieving a smaller standard deviation means in this context.




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I thought that you would draw out the normal model, but after that I really have no clue what to do. Please Help me !

 

[wildman]

Somewhere in your textbook there is a table of the Normal Distribution. Find it. You are going to need it. The table is adjusted for a mean of 0 and a standard deviation of 1. Obviously, that is not your mean or standard deviation so you will have to fix that. The way you do that is as follows where a is your value that you are trying to find the probability of:

P{x <= a} = G((a-mean)/standard deviation). Then you look up the number you have inside G() in the table.

Some tricks:

1. G(-x) = 1-G(x)

2. The table may or may not want you to add 1/2 to the values. If it starts off at 1/2 then you don't have to. If it doesn't then add 1/2.

Try your problem now, write down what you do and I or someone else will help you...