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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

When a dart is thrown at a circular target, consider the location of the landing point relative to the bull鈥檚 eye. Let \({\rm{X}}\) be the angle in degrees measured from the horizontal, and assume that \({\rm{X}}\) is uniformly distributed on \(\left( {{\rm{0, 360}}} \right){\rm{.}}\)Define\({\rm{Y}}\)to be the transformed variable \({\rm{Y = h(X) = (2\pi /360)X - \pi ,}}\) so \({\rm{Y}}\) is the angle measured in radians and\({\rm{Y}}\)is between \({\rm{ - \pi and \pi }}\). Obtain \({\rm{E(Y)}}\)and\({{\rm{\sigma }}_{\rm{y}}}\)by first obtaining E(X) and \({{\rm{\sigma }}_{\rm{X}}}\), and then using the fact that \({\rm{h(X)}}\) is a linear function of \({\rm{X}}\).

Let \({\rm{X}}\) denote the temperature at which a certain chemical reaction takes place. Suppose that \({\rm{X}}\) has pdf

\(f(x) = \left\{ {\begin{aligned}{{}{}}{\frac{1}{9}\left( {4 - {x^2}} \right)}&{ - 1拢x拢2} \\0&{{\text{ }}otherwise{\text{ }}}\end{aligned}} \right.\)

a. Sketch the graph of \({\rm{f(x)}}\).

b. Determine the cdf and sketch it.

c. Is \({\rm{0}}\) the median temperature at which the reaction takes place? If not, is the median temperature smaller or larger than\({\rm{0}}\)?

d. Suppose this reaction is independently carried out once in each of ten different labs and that the pdf of reaction time in each lab is as given. Let \({\rm{Y = }}\) the number among the ten labs at which the temperature exceeds \({\rm{1}}\). What kind of distribution does \({\rm{Y}}\) have? (Give the names and values of any parameters.)

The error involved in making a certain measurement is a continuous rv \({\rm{X}}\) with pdf

\({\rm{f(x) = \{ }}\begin{array}{*{20}{c}}{{\rm{.09375(4 - }}{{\rm{x}}^2})}&{{\rm{ - 2}} \le {\rm{x}} \le {\rm{2}}}\\{\rm{0}}&{{\rm{otherwise}}}\end{array}\)

a. Sketch the graph of \({\rm{f(x)}}\).

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If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is a. Within \(1.5\)SDs of its mean value? b. Farther than \(2.5\)SDs from its mean value? c. Between \(1 and 2\)SDs from its mean value?

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\(\begin{array}{*{20}{l}}{82.8 11.6 359.5 502.5 307.8 179.7}\\{242.0 26.5 244.8 304.3 379.1}\\{212.6 229.9 558.9 366.7 204.6}\end{array}\)

Use the corresponding percentiles of the exponential distribution to construct a probability plot. Then explain why the plot assesses the plausibility of the sample having been generated from an exponential distribution
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