Customers at Fred’s Cafe win a 100 dollar prize if their cashregister receipts s

Question

Customers at Fred’s Cafe win a 100 dollar prize if their cashregister receipts
show a star on each of the five consecutive days Monday,·· · , Friday in any
one week. The cash register is programmed to print stars on arandomly
selected 10% of the receipts. If Mark eats at Fred’s onceeach day for four
consecutive weeks and the appearance of stars is an independentprocess,
what is the standard deviation of X, where X is the number ofdollars won
by Mark in the four-week period?

Don't know how to show work.   Answer is .63

Explanation / Answer

From the binomial distribution, we have the mean of thedistribution is np and the standard deviation is npq and in the given problem, we have n = 5 and p =1/10=0.1.Andthe mean is 5*0.1=0.5 and the standard deviation is5*0.1*0.9=0.45=0.67.

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