Including forecasting demand, preparing the production schedule, estimating
costs, and preparing the budget. Project schedulers have found that
the time
required to complete a budget is normally distributed with a mean
of 8 days
and a standard deviation of 2 days. To arrange financing at the
current rate of
interest, the treasurer must know the budget within 5 days of
beginning the
process. Otherwise, a penalty will be imposed by the bank.
a) What is the probability that a budget is finished within 5
days?
b) How many days are necessary so that there is 95% chance to
complete budget within that number of days?
c) Suppose 10 budgets have to be scheduled. What is the probability
that
at least 8 budgets will be subjected to a penalty?
a) X = time taken for budget to finish
Z = (X - mean)/sd = (X - 8)/2
P(X < 5)
= P(Z < ( 5 -8)/2 )
= P(Z < -1.5)
= 0.066799
b)
P(X < x) = 0.95
P(Z
X = 8 + 1.645 * 2
= 11.29
c)
probability of penalty = 1 - 0.0668 = 0.9332
Y = the number of budget which will be subjected to a
penalty
P(Y >= 8)
Y follow binomial distribution with n = 10 , p = 0.9332
==binom.dist.range(10,0.9332,8,10)
=0.97494
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