Crystal Computer Company is considering using extra space in its retail store to introduce a new video product. Based on customer behavior toward other new products, Crystal calculates the expected value of daily profit from sales of the new product to be $200. However, Crystal must also hire a consultant to install and service the new product as part of the package customers receive. This consultant will work any number of hours per day at $40 per hour (this value includes fringe benefits). These wages would be the only additional cost to Crystal. Assume that the availability of the consultant is independent of sales (it does not affect the probability distribution of sales).
a. How many hours should
this salesperson average per day, if Crystal wants to
avoid
losing money while having the consultant available as many hours per day
as possible?
Explain your answer.
b. If the standard deviation
of the daily profit random variable is $40, how many
daily
hours should the sales person average so that Crystal is almost certain
to
not lose
money? Explain using the Empirical rule. What assumption
must you
make
to do this?
c. If the standard deviation
of the daily profit random variable is $20, how many
daily
hours should the sales person average so that Crystal is almost certain
to
not lose
money? Explain using the Empirical rule.
d. Is the assumption of independence
of consultant availability and sales
reasonable?
Explain.
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1. @STANDARDIZE(x, m, s) = (x-m)/s
2. @BINOMDIST(x, n, p, FALSE) = P(X=x) TRUE = 1 and FALSE = 0
@BINOMDIST(x, n, p, TRUE) = P(X < x)
3. @NORMSDIST(z)The S between NORM and DIST is for STANDARD.
@NORMSINV(p)
4. @NORMDIST(x, m, s, TRUE) = P(X < x)
@NORMDIST(x, m, s, FALSE) = f(x)
5. @NORMINV(p, m,
s)
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