I\'m not really sure about what variance is and I have this question Find the va

Question

I'm not really sure about what variance is and I have this question

Find the variance of Y

a) You have 5 box with 4 microprocessors in each box. They all come from a batch that as a 12,5% chance of being defective.
Y = number of box with less than 2 defective microprocessor.

b) The number of errors in a page follow a Poisson distribution where =1.05 .
Y = number of pages without error in the first 110 pages.

c) The weight of fruits in a stand are on average of 74,5g and of have a standard deviation of 0,35g.
Y= the total weight of 12 fruits pick ramdomly.

d) The weight of fruits in a stand are on average of 74,5g and of have a standard deviation of 0,35g.
Y= the average weight of 12 fruits pick ramdomly.

Explanation / Answer

Solution:

a. Since it is a binomial distribution with n = 20 and p = 0.125, the variance is np (1 – p) = 20*0.125*(1 – 0.125) = 2.1875

b. Since it is a Poisson distribution with n = 110, =1.05, the variance is 110*1.05 = 115.5.

c. Since it is a normal distribution with = 0.35 and n = 12, the variance is (0.35)^2/12 = 0.0102

d. Since it is a normal distribution with = 0.35 and n = 12, the variance is (0.35)^2/12 = 0.0102

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