An experiment consists of rolling a fair die 8 times and rec

An experiment consists of rolling a fair die 8 times and recording the number of times a 3 occurs? The usual number of times a 3 occurs is: Sample items are popular in supermarkets. Costumer take free samples in about 60% of the cases. When 317 costumers are observed, what is the probability that more than 180 will take a sample? Do you try to pad an insurance claim to cover your deductible? About 40% of all U.S. adults will try to pad their insurance claim this year. A director of an insurance adjustment office has just received 128 insurance claims to be processed. What is the probability that more than 80 of the claims are not padded? 51.2% 32% 25.1% 28.1% 26.7%

Solution

3.

The probability of a 3 is 1/6.

Thus,

u = mean number of 3\'s = n p = 8*(1/6) = 1.3333333.

The standard deviation is

s = sqrt(n p (1-p)) = sqrt(8*(1/6)*(1-1/6)) = 1.054092553

Thus, the usual values lie within 2 standard deviations from the mean,

u - 2s = 1.33333333 - 2*1.054092553 = -0.774851776
u + 2s = 1.33333333 + 2*1.054092553 = 3.441518436

Thus, the integers between these values are 0,1,2,3. [OPTION C]

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