economics

SampleProblems_Finalsolution.xlsx

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Q3

A utility company wants to catgotize its customers in three categories - low bills, medium bills and high bills.
The bills below $50 are low, above 150 high and in between medium.
The data was collected and a histogram was plotted. It determined that the data is distributed as a Normal
distribution whose mean and stadard devaition are 100 and 25 respectively.	Mu	100
	Sigma	25
a) What is the probability of a customerto be in the low category?	P (X<50)	0.0227501319
b) What proportions of the customers are in the medium category?	P (50 < X<150)	0.9544998681
c) What percentage of the customers are in the high category?	P (X>150	0.02275
d) How much a customer must spend to be in the bottom 5%?	P (X<x?) =.05	58.8786593262

Q4

In reference to Problem 3, a random sample of 25 customers was taken.

100

SigmaofXBAR

sigma

What is the probability that the sample mean is below $95?

P (XBAR <95)

0.1586552539

b. What proportion of the sample mean are above $110?

P (XBAR>110)

0.0227501319

c. What percentage of the sample mean be between $95 and $110?

0.8185946141

If the data was not distributed as a Normal Distribution, would you be able to answer the above questions?

No,theample sizemust be at least30)

Q5

Data was collected to study the background of the people who participate in the stock market.

49 customers were selected at random and asked about their annual savings and whether they lived in a suburb.

After the sample was collected, the data was analyzed to calculate sample mean annual savings , sample standard deviation and the sample proportion

of people living in a suburb

Sample mean = $10K

Sample Standard Deviation = $3K

Sample Proportion = 0.4

Sample Mean Standard deviation

0.4285714286

t for0.025and48df

1.6772241961

Calculate the 90% confidence limits for the Annual Savings.

0.7188103698

9.2811896302

Upper Limit

10.7188103698

Lower Limit

The interval 9.28 and 10.72 contains the true population mean 90% ofthetime

Calculate the 95% confidence limits for the population proportion living in suburbs

1.96

0.4

upper limit

0.5371714256

p(1-p)

0.24

Lower Limit

0.2628285744

p (1-p)/n

0.0048979592

The true percentage of people living in suburbs is in the range 26 and 54 95% ofthetime.

SQRT()

0.0699854212