TWINTECH COLLEGE SARAWAK
DDG 2213
BUSINESS STATISTICS
IN CLASS EXERCISES 5
1.
Given a standardized normal distribution (with a mean of 0 and a standard
of 1), determine the following probabilities :
a.
b.
c.
d.
e.
2.
deviation
P(Z > +1.08)
P(Z < -0.21)
P(-1.96 < Z < -0.21)
P(-1.96 < Z < +1.08)
P(+1.08 < Z < +1.96)
The New York Times reported that the average time to download the home page from the
Internal Revenue Service Web site www.irs.gov was 0.8 seconds. Suppose
that
the
download time was normally distributed with a standard
deviation of 0.2 seconds. What
is the probability that a download time will be :
a.
b.
c.
d.
less than 1 second?
between 0.5 and 1.5 seconds?
above 0.5 second?
99 % of the download times will be above how many seconds?
The same article also reported that the average download time for the H&R Block Web site
www.hrblock.com was 2.5 seconds. Suppose that the download time
was
normally
distributed with a standard deviation of 0.5 seconds. What is the probability
that
a
download time will be :
e.
f.
g.
h.
3.
less than 1 second?
between 0.5 and 1.5 seconds?
above 0.5 second?
99 % of the download times will be above how many seconds?
During 2001, 61.3% of U.S. households purchased ground coffee. Moreover,
these
households spent on average of $36.16 on ground coffee during the year.
Consider
the annual ground coffee expenditures for households purchasing ground coffee, assuming
that these expenditures are approximately distributed
as a normal random variable
with a mean of $36.16 and a standard deviation of $10.00.
a.
b.
c.
d.
e.
f.
Find the probability that a household spent less than $25.00.
Find the probability that a household spent more than $50.00.
Find the probability that a household spent more than $75.00.
What proportion of he households spent between $30.00 and $40.00?
99% of the households spent less than what amount?
80% of the households spent more than what amount?
4.
An orange juice producer buys all his oranges from a large orange groove. The amount of
juice squeezed from each of these oranges is approximately normally
distributed with a
mean of 4.70 ounces and a standard deviation of 0.40 ounces.
a.
b.
c.
5.
What is the probability that a randomly selected orange will contain between 4.70
and 5.00 ounces?
What is the probability that a randomly selected orange will contain between 5.00
and 5.50 ounces?
77% of the oranges will contain at least how many ounces of juice?
Packets are filled automatically by packing machine. The amount dispensed by the
machine has a normal distribution with the mean 259 g and standard 5g. After being filled,
the packets are weighted and those weighting less than 250g are rejected as underweight.
Packet weighting more more than 267 g are rejected since they are liable to burst. Each
rejected packet costs the company 20 cents. The machine fills 10000 packets each month.
a) find the probability that a randomly selected packet weight
a. less than 250g
b. more than 267 g
c. Calculate the average monthly cost of rejected.
b) A new machine is available and the amount dispersed by this machine has a normal
distribution with mean 259, s.d 4g. Calculate the average monthly saving cost of
rejected packets that would result from this machine rather than the original one.
a. Less than 250g
b. More than 267 g
c. The probability rejected by the new machine
6. The lifetime of an electrical component is normally distributed with mean 2000 hours and
s.d 400 hours. The manufacturer guarantees the components with last for 20 weeks when
used10 hours a day seven day a week
a. Calculate the proportion if components which fall within the guarantee period
b. To what value must the guarantee period be changed if only 3% of components are
fall within the guarantee period?
7. Suppose x is a normal distribution with mean 70 and variance 4. find
a. P ( x  74)
b. P67  x  75
c. P (71  x  72)
d. P(63  x  68)