Download - Stats Solutions Danny
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1. Poisson DistributionProblem
Southwestern Electronics has developed a new calculator that performs a series of functions
not yet performed by any other calculator. The marketing department is planning to
demonstrate this calculator to a group of potential customers, but is worried about some
initial problems, which have resulted in 4 percent of the new calculators developing
mathematical inconsistencies. The marketing VP Is planning on randomly selecting a group
of calculators for this demonstration and is worried about the chances of selecting a
calculator that could start malfunctioning. He believes that whether or not a calculator
functions is a Bernoulli process and he is convinced that the probability of malfunction is
really about 0.04.
a. Assuming that the VP selects exactly 50 calculators to use in the demonstration, andusing the Poisson distribution as an approximation of the binomial, what is the chance of
getting at least three calculators that malfunction?
b. No calculators malfunctioning?Solution
n = 50
p = 0.04
= np = 2
= 0.13533
Formula: P(X=) =
P ( =0) =
= 0.13533
P ( =1) =
= 0.27066
P ( =2) =
= 0.27066
P ( =3) =
= 0.18044
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P ( 3) = 1 P ( 2)
= 1 [P ( =0) + P ( =1) + P ( =2)]
= 1 [0.13533 + 0.27066 +0.27066]
= 0.32335
Answer
a.) The chance of getting at least three calculators that malfunction is 32.33%b.) The chance of no calculators malfunctioning is 13.53%
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2. Hypothesis Testing (Single Population)Problem
General Electric has developed a new bulb whose design specifications call for a light output
of 960 lumens compared to an earlier model that produced only 750 lumens. The companys
data indicate that the standard deviation of light output for this type of bulb is 18.4 lumens.
From a sample of 20 new bulbs, the testing committee found an average light output of 954
lumens per bulb. At a 0.05 significance level, can General Electric conclude that its new bulb
is producing the specified 960 lumen output?
Solution
= 18.4
n = 20 = 954 = 960 = 0.05 = 960
= 960
< 960
= - 1.65
=
=
= - 1.45
Answer
Do not reject . The new bulb is meeting specifications.
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3. Hypothesis Testing (Single Population)Problem
BSNL provides telephone services in Coimbatore. According to the companys records the
average length of calls placed through the company is 11.44 minutes. The company wants to
check if the mean length of the current calls is different from 11.44 minutes. A sample of 150
such calls placed through this company gave a mean length of 12.71 minutes with a standard
deviation of 2.65 minutes. Can you conclude that the mean length of all current calls is
different from 11.44 minutes? Use = 0.05.
Solution
s = 2.65
n = 150 = 12.71 = 11.44 = 0.05
= 11.44
11.44
= 1.65
=
=
= 5.87
Answer
Reject . It is concluded that the mean length of current calls is different from 11.44minutes.
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4. Hypothesis Testing ( Two populations)Problem
A credit-insurance organization has developed a new high-tech method of training new
sales personnel. The company sampled 16 employees who were trained the original way and
found average daily sales to be $688 and the sample standard deviation was $32.63. They
also sampled 11 employees who were trained using the new method and found average
daily sales to be $ 706 and the sample standard deviation was $24.84. At alpha = 0.05, can
the company conclude that average daily sales have increased under the new plan?
Solution
n1 = 16 n2 = 11 n = n1 + n2 = 27
1 = 688 2 = 206
1 = 32.63 2 = 24.84
= 0.05
1 - 2 = 0
1 - 2 0
= - 1.708
=
=
= 885.64
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=
=
= - 1.545
Answer
Do not reject . Average daily sales have not increased significantly.