[Solved] Reading: Class notes and Chapter 5 of the class textbook - #80099
Reading: Class notes and Chapter 5 of the class textbook (Introduction to the Practice of Statistics, by Moore et. al. 4th edition)
Please complete and submit the following:
(total: 50pts)
Exercise 1:
“In a process for manufacturing glassware, glass stems are sealed by heating them in a flame. The temperature of the flame varies a bit. Here is the distribution of the temperature X measured in degrees Celsius:
|
Temperature |
540o 545o 550o 555o 560o |
|
Probability |
0.1 0.25 0.3 0.25 0.1 |
(a) Find the mean temperature \({{\mu }_{X}}\) and the standard deviation \({{\sigma }_{X}}\).
(b) The target temperature is 550o C. What are the mean and standard deviation of the number of degrees off target, X-550?
(c) A manager asks for results in degrees Fahrenheit is given by
Y=(9/5) X +32
What are the mean \({{\mu }_{Y}}\) and standard deviation \({{\sigma }_{Y}}\) of the temperature of the flame in degrees Fahrenheit scale?”
Exercise 2: (Binomial distribution) Use Table C
“A university that is better known for its basketball program than for its academic strength claims that 80% of its basketball players get degrees. An investigation examines the fate of all 20 players who entered the program over a period of several years that ended 6 years ago. Of these players, 11 graduated and the remaining 9 are no longer in school. If the university’s claim is true, the number of players who graduate among the 20 studied should have the B(20,0.8) distribution.
(a) Find the probability that exactly 11 of the 20 players graduate.
(b) Find the probability that 11 or fewer players graduate. This probability is so small that it casts doubts on the university’s claim.”
(Hint: In both questions, 11 graduating is the same as 9 failing when looking at 20 students. Failures have the B(20,0.2) distribution which is available in Table C).
Exercise 3:
A student organization is planning to ask a sample of 50 students if they have noticed alcohol abuse brochures on campus. The sample percentage who say “Yes” will be reported. The organization’s statistical advisor says that the standard deviation of this percentage will be about 7%.
(a) What would the standard deviation be if the sample contained 100 students rather than 50?
(b) How large a sample is required to reduce the standard deviation of the percentage who say “Yes” from 7% to 3.5%? Explain to someone who knows no statistics the advantage of taking a larger sample in a survey of opinions.
Exercise 4: (#2 p.327)
Four hundred draws will be made at random with replacement from the box:
|1 3 5 7|
(a) (7pts) Estimate the chance that the sum of the draws will be more than 1,500.
(b) (8pts) Estimate the chance that there will be fewer than 90 3’s (hint: need new box here!)
Exercise 5: (#1 p.391)
The Residential Energy Consumption Survey found in 1990 that 14.8% of American households had a computer. A market survey organization repeated this study in a certain town with 25,000 households, using a simple random sample of 500 household: 79 of the sample households had computers.
(a) The percentage of households in the town with computers is estimated as:_________;
(b) this estimate is likely to be off by ______ or so (this is the SE%).
Deliverable: Word Document
and pdf
