Consider the following sample of observations on coating thickness for low-viscosity paint. 0.83   0.88   0.88   1.03   1.09   1.21   1.29   1.31 1.42   1.49   1.59   1.62   1.65   1.71   1.76   1.83 Assume that the distribution of coating thickness is normal (a normal probability plot strongly supports this assumption). (c) Calculate a point estimate of the value that separates the largest 10% of all values in the thickness distribution from the remaining 90%. [Hint: Express what you are trying to estimate in terms of μ and σ.] (Round your answer to four decimal places.)   (d) Estimate P(X < 1.2), i.e., the proportion of all thickness values less than 1.2. [Hint: If you knew the values of μ and σ, you could calculate this probability. These values are not available, but they can be estimated.] (Round your answer to four decimal places.)   (e) What is the estimated standard error of the estimator that you used in part (b)? (Round your answer to four decimal places.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Consider the following sample of observations on coating thickness for low-viscosity paint.

0.83   0.88   0.88   1.03   1.09   1.21   1.29   1.31
1.42   1.49   1.59   1.62   1.65   1.71   1.76   1.83

Assume that the distribution of coating thickness is normal (a normal probability plot strongly supports this assumption).

(c) Calculate a point estimate of the value that separates the largest 10% of all values in the thickness distribution from the remaining 90%. [Hint: Express what you are trying to estimate in terms of μ and σ.] (Round your answer to four decimal places.)

 

(d) Estimate P(X < 1.2), i.e., the proportion of all thickness values less than 1.2. [Hint: If you knew the values of μ and σ, you could calculate this probability. These values are not available, but they can be estimated.] (Round your answer to four decimal places.)

 

(e) What is the estimated standard error of the estimator that you used in part (b)? (Round your answer to four decimal places.)

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