Problems 13-17. The number of defects for various numbers of batches of DVDs at

Question

Problems 13-17. The number of defects for various numbers of batches of DVDs at a manufacturer were recorded in the table below.

Defects 0 1 2 3 4 5

Batches 95 113 87 64 13 8 14.

Use the frequency distribution to construct a probability distribution.

15. What is the mean of the probability distribution? 2

16. What is the variance of the probability distribution?

17. What is the standard deviation of the probability distribution?

18. Interpret the results in the context of the real-life situation (See the interpretation in worked example 6 in the text). You must say something about both the mean and the variation for this distribution.

Explanation / Answer

In this problem, the underlying r.v. is

x = the number of defects per batch of camping chairs inspected.

Construct a probability distribution.

It is given that Defects 0 1 2 3 45 Batches 95 113 87 64 13 8 The sum of the second row is 380. Divide each number in the second row by 380 and relabel the rows as follows: x 012345 P (x) .250 .297 .229 .168 .034 .021

That is, if we choose at random one of the 380 batches of chairs, the probability that batch has x = 0 defects is 0.250.

We calculate the mean, variance, and standard deviation. We enter the probability distribution into two lists. L1 012345 L2 .250 .297 .229 .168 .034 .021 Now, entering 1-Var Stats L1,L2, we see that = 1.5, 2 x 1.54, x 1.24 . (The value of 2 x was obtained squaring the value of x.)

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