Question

4) An entry-level accountant is expected to work long hours during the accounting firm's "busy season". Let X be the number of hours per day an entry level accountant works. X can be described by a normal distribution with mean 12.9 hours and standard deviation 2.4 hours. a) find the mean and standard deviation for the sampling distribution of an entry-level accountant's average daily hours for the month of January (31 days). B) what is the probability that the entry-level accountant's average number of hours worked per day for the month of January is between 12 and 14 ? c) what is the probability that the entry-level accountant worked more than 15 hours on any given day in January? d) /how many hours does an entry-level accountant work during the longest 15% of days?

Answer 1

a) maean of sampling distrbution μx=12.9

and standard deviation for the sampling distribution σx̅=σ/√n=2.4/sqrt(31)=0.4311

b)_

for normal distribution z score =(X-μ)/σ

probability that the entry-level accountant's average number of hours worked per day for the month of January is between 12 and 14

probability =

P(12<X<14)

=

P(-2.09<Z<2.55)=

0.9946-0.0183=

0.9763

c)

probability that the entry-level accountant worked more than 15 hours on any given day in January :

probability =

P(X>15)

=

P(Z>0.88)=

1-P(Z<0.88)=

1-0.8106=

0.1894

d)

for 85th percentile critical value of z=		1.04
therefore corresponding value=mean+z*std deviation=			15.40