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Probability for Accumulated Snowfall

Problem 1
Molly Dymond and Kathleen Taylor are considering the possibility of teaching swimming to kids during summer. A local swim club opens its pool each day so it is available
to rent during the morning. The cost of renting the pool during the 10-week period for which Molly and Kathleen would need it is $1,700.
The pool would also charge Moly and Kathleen an admission, towel service, and life guard fee of $7 Per pupil...and molly and Kathleen estimate an additional $5 cost per student to hire several assistants.
Molly and Kathleen plan to charge $75 per student for the 10 week swim class.
a) how many pupils do Molly and Kathleen need to enroll in their class to break even?
b)If Molly and Kathleen want to make a profit of $5,000 for the summer, how many pupils do they need to enroll?
c) Molly and Kathleen estimate that they might not be able to enroll more than 60 pupils. If they enroll this many pupils, how much
would they need to charge per pupil in order to realize their profit goal of $5,000?

Problem 2
Downhill Ski resort in colorado has accumulated info from records of the past 30 winters regarding the measurable snowfall. This info is as follows:

Snowfall(in) Frequency
0-19 2
20-29 7
30-39 8
40-49 8
50+ 5

a) Determine the probability of each event in this frequency distribution
b)Are all the events in this distribution mutually exclusive? Explain

Problem 3
The quality control process at a manufacturing plant requires that each lot of finished units be sampled for defective items. 20 units from each lot
are inspected. If five or more defective units are found, the lot is rejected. If a lot is known to contain 10% defective items, what is the probability that the lot will be rejected? Accepted?

Problem 4
A retail outlet recieves radios from three electrical appliance companies. The outlet recieves 20% of its radios form A, 40% from B, 40% from C.

The probability of receiving a defective radio from A is 0.01; from B, 0.02; and from C, 0.08.
a) Develop a probability tree showing all marginal, conditional and joint probabilities.
b)Develop a joint probability table.

Problem 5
The grade point average of students at a university is normally distributed, with a mean of 2.6 and a standard deviation of 0.6.
A recruiter for a company is inteviewing students for summer employment. What percentage of the students will have a a grade point average of 3.5 or greater?

Problem 6
The owner of Western Clothing Company has determined that the company must sell 670 pairs of denim jeans each month to break even (i.e. to reach the point where
total revenue equals total cost).
the company marketing department has estimated that monthly demand is normally distributed, with a mean of 805 pairs of jeans and a standard deviation of 207 pairs.
What is the probability that the company will make a profit each month?


Solution Preview

Please see the attached file.

Problem 1.
Given rent of the pool for the ten week period = $1,700
Addition cost per student = $7 + $ 5 = $12
Fee planned to charge per student for the ten week = $ 75
a) Suppose n students are enrolled.
Then the total cost of the program =
Total income that can be earned = 75n
To make the program break even total cost must be equal to total income

Molly and Kathleeen require 27 students to be enrolled in order to make the program break even.
b) Suppose n students are enrolled.
Total income required so as to make a profit of $5000 =
Total income that can be earned = 75n

Molly and Kathleeen require 107 students to be enrolled to make a profit of $5000.
c) Maximum students that can be enrolled = 60
Total income required so as to make a profit of $5000 = = ...

Solution Summary

The probability for accumulated snowfall is examined.