Assume that data contained in the
BUSI1013-Numerical Data A.xls
file is from a simple random sample of
customers of a Canadian retailer. Use this data to answer the following: (
4 Points
)
a.
Develop a point estimate of the mean number of transactions for the retailer.
b.
Develop a point estimate of the population standard deviation of the number of transactions.
1.
a)
x = ∑xi / n
- x = 1298 / 30 = 43.26
- Therefore the point estimate mean for the number of transactions = 43.26
b)
s = (SQRT of ∑(xi – x)^2 / n-1
- s = (SQRT of 5115.87 / 29)
- s = (SQ of 176.41) = 13.33
- Therefore the point estimate standard deviation for the number of transactions is 13.33
The average waiting time for customers at a fast food restaurant is 3.5 minutes. The population standard
deviation is 2.2 minutes. (
6 Points
)
a.
Assume that the waiting time of customers at this restaurant follow a normal distribution, what
is the probability that a simple random sample of 60 customers will have a sample waiting time
of less than 3 minutes?
b.
Do we need to make any assumption on the distribution of waiting times for the calculation in
Part a? Why or why not?
c.
What is the probability that a simple random sample of 120 customers will have a sample
waiting time of less than 3 minutes?
2.
a)
P(x < 3)
- Ox = o / (SQRT of n)
- Ox = 2.2 / 7.75 = 0.28
- z = x – u / o

- z = 3 – 3.5 / 0.28 = -1.79
- Using Standard Table: - 1.79 = 0.0367
- Therefore the probability that the sample of 60 customers will wait less than 3 minutes = 0.0367
b)
Yes, we had to assume that the population was infinite, making it appropriate to need to compute a
new standard deviation for the given sample population
- We also assumed that the restaurant follows a normal distribution, allowing a standard normal
conversion and calculation to be made to find the probability.
c)
Ox = o / (SQRT of n)
- Ox = 2.2 / 10.95 = 0.2
- z = 3 – 3.5 / 0.2 = -2.5
- Using the standard table: -2.5 = 0.0062
- Therefore the probability that the sample of 120 customer’s will wait less than 3 minutes = 0.0062
Traditionally, 30% of customers of a cell phone company leave after their term contract expires. If this is
the true population proportion of churn (customers leaving after their term expired), answer the
following questions: (
6 Points
)
a.
If simple random samples of 100 customers are taken from the population of customers of this
company, describe the sampling distribution of the sample proportion of churn.

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- Winter '15
- Business, Normal Distribution, Standard Deviation