Q- A manufacturing producing a product time is normally distributed. A random sa
ID: 3070638 • Letter: Q
Question
Q- A manufacturing producing a product time is normally distributed. A random sample has a mean of 40 minutes and a standard deviation of five minutes. Estimate the percent of products that are produced between 35 and 40 minutes. The first step in solving this problem is to calculate the Z scores
(in the previous example I provided the Z-Scores for you, this time you will have to calculate them first. This is a simple process once you have the formula). The Z-score formula is as follows: Z = x-/)
(In this example, X= 35, 40 minutes, and = 30, and =5) Remember you need the Z score for 35 minutes and the Z score for 40 minutes
What are the calculated Z-scores for
X= 35? ____________
X= 40? ____________
Using the Appendix II on page 711 of the text or Minitab, or Excel, what is the
area under the curve for the above calculated Z-scores?
Area under the curve for Z-score X=35? ______________
Area under the curve for Z-score X=40? ______________
What is the difference, in other words, what is the approximate percentage of
time that this manufacturer can produce a product between 35 and 40 minutes
based on the data that you were given and your calculations of the z-score using
the normal distribution table? _______________
Based upon your answer do you believe this manufacture as the capability to
consistently produce a product between 35 and 40 minutes?
(Note: the answer has to be typed, not hand written nor in a picture.) Thank you.
Explanation / Answer
Given that
= 40, and =5
p ( 35 < x < 40 ) =?
sol :
p ( 35 < x < 40 )
= p( (35 - 40) / 5 < z < ( 40 - 40) / 5 )
= p ( -1 < z < 0 )
= p ( z <0 ) - p ( z < -1 )
= 0.5 - 0.1587
= 0.3413 or 34.13%
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