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Chapter 4: Q87E (page 192)

The accompanying normal probability plot was constructed from a sample of \({\rm{30}}\) readings on tension for mesh screens behind the surface of video display tubes used in computer monitors. Does it appear plausible that the tension distribution is normal?

Short Answer

Expert verified

Yes, itappears plausible that the tension distribution is normal.

Step by step solution

01

Definition of Probability

The normal probability plot is a graphical tool for detecting significant deviations from normality. Outliers, skewness, kurtosis, the necessity for transformations, and mixes are all examples of this. Raw data, residuals from model fits, and estimated parameters are used to create normal probability charts. A graph of normal probability.

02

Step 2: Explanation of the tension distribution is normal

The pattern in the following normal probability plot is relatively straight, implying that the stress distribution is likely to be normal.

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Most popular questions from this chapter

Let X denote the number of flaws along a \({\bf{100}}\)-m reel of magnetic tape (an integer-valued variable). Suppose X has approximately a normal distribution with m \(\mu = 25\) and s \(\sigma = 5\). Use the continuity correction to calculate the probability that the number of flaws is

a. Between \({\bf{20}}\) and \({\bf{30}}\), inclusive.

b. At most \({\bf{30}}\). Less than \({\bf{30}}\).

In each case, determine the value of the constant\({\rm{c}}\)that makes the probability statement correct. a.\({\rm{\Phi (c) = }}{\rm{.9838}}\)b.\({\rm{P(0}} \le {\rm{Z}} \le {\rm{c) = }}{\rm{.291}}\)c.\({\rm{P(c}} \le {\rm{Z) = }}{\rm{.121}}\)d.\({\rm{P( - c}} \le {\rm{Z}} \le {\rm{c) = }}{\rm{.668}}\)e.\({\rm{P(c}} \le {\rm{|Z|) = }}{\rm{.016}}\)

The accompanying observations are precipitation values during March over a \(30\)-year period in Minneapolis-St. Paul.

\(\begin{array}{*{20}{l}}{.77\;\;1.20\;\;3.00\;\;1.62\;\;2.81\;\;2.48}\\{1.74\;\;.47\;\;3.09\;\;1.31\;\;1.87\;\;\;\;.96}\\{.81\;\;1.43\;\;1.51\;\;\;\;.32\;\;1.18\;\;1.89}\\{1.20 3.37\;\;2.10\;\;\;\;.59\;\;1.35\;\;\;\;.90}\\{1.95 2.20\;\;\;\;.52\;\;\;\;\;.81\;\;4.75\;\;2.05}\end{array}\)

a. Construct and interpret a normal probability plot for this data set. b. Calculate the square root of each value and then construct a normal probability plot based on this transformed data. Does it seem plausible that the square root of precipitation is normally distributed? c. Repeat part (b) after transforming by cube roots.

The weight distribution of parcels sent in a certain manner is normal with mean value\({\rm{12lb}}\)and standard deviation\({\rm{3}}{\rm{.5lb}}\). The parcel service wishes to establish a weight value\({\rm{c}}\)beyond which there will be a surcharge. What value of\({\rm{c}}\)is such that\({\rm{99\% }}\)of all parcels are at least\({\rm{1lb}}\)under the surcharge weight?

A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is \({\rm{.500}}\)in. A bearing is acceptable if its diameter is within \({\rm{.004}}\)in. of this target value. Suppose, however, that the setting has changed during the course of production, so that the bearings have normally distributed diameters with mean value \({\rm{.499}}\)in. and standard deviation \({\rm{.002}}\)in. What percentage of the bearings produced will not be acceptable?
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