1. A sample of 20 glass bottles of a particular type was selected, and the inter

Question

1. A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. Consider the following partial sample information: Median = 202.2 lower fourth 196.0 Upper fourth 216.8 Three smallest observations Three largest observations 125.8 221.3 188.1 230.5 193.7 250.2 Are there any outliers in the sample? Any extreme outliers? Justify your answer. 2. A certain sports car comes equipped with either an automatic or a manual transmission, and the car is available in one of four colors. Relevant probabilities for various combinations of transmission type and color are given in the accompanying table. Color Blue .10 Red White .13 .15 Transmission Type Black 18 Let A (automatic transmission), B-/black), and C= (white). Calculate P(A), P(B), and P(A n B). h a. Calculate both PIA B) and P(B / A), and explain in context what each of these probabilities b. represents. c. Are the events "Automatic Transmission" and "Black independent? Justify your answer 3. . A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 5-lb patches. Let X the number of batches ordered by a randomly chosen customer and suppose that X has pm p/x) 2 4 3 1 Compute the expected number of batches ordered

Explanation / Answer

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Solution:

Are there any outliers in the sample?

First we need to find the inner fences,
Inter quartile range, IQR = UQ - LQ = 216.8 - 196 = 20.8
Inner fences = (LQ - 1.5*IQR, UQ + 1.5*IQR) = (196 - 1.5*20.8, 216.8 + 1.5*20.8) = (164.8, 248)
If any point lies below the lower inner fence or above the upper inner fence, they are outliers.

Outliers are 125.8 and 250.2

Any extreame outliers?

Here we have to find the outer fences,
Inter quartile range, IQR = UQ - LQ = 216.8 - 196 = 20.8
Outer fences = (LQ - 3*IQR, UQ + 3*IQR) = (196 - 3*20.8, 216.8 + 3*20.8) = (133.6, 279.2)
If any point lies below the lower iouterr fence or above the upper outer fence, they are extreme outliers.

Extreme Outliers: 125.8

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