In: Statistics and Probability

**You want to know how the commuting time of your
employees compare to Departments competing for the same staff, so
you get some survey data on average commuting times for 25 randomly
selected people in your line of business.**

**Data: 59, 74, 73, 66, 80, 84, 90, 122.5, 37.2, 50,
139.3, 39, 80, 35, 88, 34, 82, 65, 61, 63, 66, 88, 70, 79,
75**

**You find that the mean commuting time is 72 minutes,
with a standard deviation of 24.53. (Check for
yourself!)**

**a) Calculate your standard error. (3 pts.)**

**b) Based on this, calculate a 95 percent Confidence
Interval for the mean commuting time. (Remember, the C.I. is
calculated by adding and subtracting from the observed sample mean
the product of the standard error and the appropriate t-value; for
the latter, you may use Excel tinv) Show your work. (7
pts.)**

**b) Given the data in the question above about mean
commuting time, calculate the 90% Confidence Interval. (Again, show
your work. (5 pts.)**

**c) Which is a bigger range, the 95% or 90% confidence
interval? Why? (3 pts.)**

**d) What assumptions must you make about the population
when constructing confidence interval estimates? (2
pts.)**

How well do you really know your customers? And how well did
they want to know you right?

3. The time spent commuting from home to work for all employees
of a very large company has a normal distribution with a mean of
43.4 minutes and a standard deviation of 12.1 minutes. Calculate
the probability that the mean time spent commuting from home to
work by a sample of 21 employees will be in between 43.26 and
49.35.

Introduction to Probability and Statistics
Scenario: We wish to compare the commuting time in minutes to
the university of two sections of a particular
Morning Section Times:
39 35 39 39 40 37 41 39 42 40 37 35 38 36 40 35 38 36 39 35 38 35
39 38 41 39 38 40 38 41 41 37 34 41 37 41 35 39 36 41
Evening Section Times:
35 47 29 34 26 34 38 45 44 49...

If you want to know how important spam filters are to your
online experience, try turning them off for a day. You’ll quickly
see why these tools we tend to take for granted are so essential.
Generally speaking, a filtering solution applied to your email
system uses a set of protocols to determine which incoming messages
are spam and which are not. What the filters checks on can vary,
but often they all do basically the same thing: scan header...

If you want to know how important spam filters are to your
online experience, try turning them off for a day. You’ll quickly
see why these tools we tend to take for granted are so essential.
Generally speaking, a filtering solution applied to your email
system uses a set of protocols to determine which incoming messages
are spam and which are not. What the filters checks on can vary,
but often they all do basically the same thing: scan header...

Suppose you are thinking about getting a puppy and want to know
the amount of time people spend caring for puppies. You survey 31
puppy owners and find that the mean amount of time they spend
caring for their puppies is 108.0 minutes per day with a sample
standard deviation of 17 minutes. Construct a 98% confidence
interval for the mean amount of time puppy owners spend on their
puppy per day. Interpret the interval. (1pt)
Point Estimate: ______
Margin...

You are a manager and you want one of your employees to receive
training. Anna is one your best workers and you believe one day she
will have your job on her way to the c-suite. You know money is
tight right now and if you don’t use your training budget (there is
currently $2,000 left) by the end of the quarter
the company will take it back. Also, you have heard rumors that the
raise pool will be low...

Assume you want to establish a set of standards for your
employees in "the handling a complaint from the company's customer
complaint line". Outline the important steps you would use in
determining what should be considered.

Assume you want to establish a set of standards for your
employees in "the handling a complaint from the company's customer
complaint line". Outline the important steps you would
use in determining what should be considered.

Your probability professor has been dedicating part of the time
she used to spend commuting to doing longer yoga practices. She
took a random sample of her yoga practices since Hofstra has ceased
in-person classes and found 3 under ten minutes and 19 over ten
minutes. Construct a 99% confidence interval for the proportion of
her yoga practices that will be over ten minutes given her current
lifestyle.

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