# Answer to Question #8814 in Quantitative Methods for Hitesh Prajapati

Question #8814
Que-1. The probability that a bulb produced by a factory will fuse after certain period of time is 0.05. Find the probability that out of 5 such bulbs a. None fuses b. Not more than 2 fuse c. More than 2 fuse Que-2. A supplier of components to an electronic industry makes a sophisticated product which sometimes fails immediately it is used. He controls his manufacturing process so that the proportion of faulty products is supposed to be only 5%. Out of 400 supplies in a batch, 26 prove to be faulty. Verify the manufacturer&rsquo;s claim. Use 0.05 level of significance. Que-3. The ages of husbands and wives in a community were found to have a correlation coefficient equal to +0.8; the average of husbands&rsquo; ages was 25 years and that of wives&rsquo; ages 22 years; their standard deviations were respectively 4 and 5 years. Find the two lines of regression and from the lines ,measure a. The expected age of husband when wife&rsquo;s age is 12 years b. The expected age of wife when husband&rsquo;s age is 33 years
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2012-04-26T07:42:50-0400
Question 3
The ages of husbands and wives in a community were found to have a
correlation coefficient equal to +0.8; the average of husbands&rsquo; ages was
25 years and that of wives&rsquo; ages 22 years; their standard deviations
were respectively 4 and 5 years. Find the two lines of regression and
from the lines ,measure
a. The expected age of husband when wife&rsquo;s age is 12 years
The answer has three factors in it.
1) Since there is 0.8 correlation coefficient, this gives 12*0.8 = 9.6; rounds to 10;
2) This leaves 0.2 that is not in correlation, and that gives 25*0.2 = 5; and
3) On the average, the husband is 3 years older.
Altogether this gives 10 + 5 + 3 = 18.
b. The age of 33 for a wife puts the husband at 0.8(33) with a standard deviaton of 0.2(4).
That is, the husband is, on the average, 26.4, with a st dev of 0.8.
That puts the husband age rougly as at least 25 and at most 27.

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