What is the probability that it takes at most 26 minutes total to produce a randomly selected part? b. What is the probability the difference in machining timing between the second and first operation (X2-X1) exceeds 6 minutes?

What is the probability that it takes at most 26 minutes total to produce a randomly selected part? b. What is the probability the difference in machining timing between the second and first operation (X2-X1) exceeds 6 minutes?

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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Question

100%

Suppose that the manufacturing of a particular part requires three
different machining operations. Machining time (X1, X2, X3) for each of the three
operations has a normal distribution and are independent from one another. The
mean values are 10, 12, and 8 minutes respectively, and standard deviations are 2,
2.5, and 1.5 respectively.

a. What is the probability that it takes at most 26 minutes total to produce a
randomly selected part?

b. What is the probability the difference in machining timing between the second
and first operation (X2-X1) exceeds 6 minutes?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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