HOMEWORK: SAMPLING DISTRIBUTIONS
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Example 1
 Consider the relation between standard deviation of the sample and standard deviation of the population
 Be sure you understand the meaning of each variable.
 Identify the given variables:
mean
standard deviation of the population
size of the sample
 With the given values you can compute the standard deviation of the mean.
Example 2
 Consider the definition of z
Z =
 Consider the relation between standard deviation of the sample and standard deviation of the population
 Identify the given variables
 need to convert from the population standard deviation to standard deviation of the mean.
Note: We consider the mean sample to be equal to the mean of the origin population.
 Find Z (for the given X)
 Find area under the curve
 Compute the final answer. Keep in mind that you need the likelihood for or more than “ X” hours.
Keep in mind that not all problems or subproblems use a sample.
Show all manual calculations and provide commentary to your answers.
PROBLEM 1 (10 points):
A laptop manufacturer finds that the average time it takes an employee to load a laptop with software is 40 minutes with a standard deviation 15 minutes. Suppose you take a random sample of 49 employees. The standard deviation of the sample mean is:
Standard Deviation 

PROBLEM 2 (15 points) :
A company that manufactures bookcases finds that the average time it takes an employee to build a bookcase is 23 hours with a standard deviation of 8 hours. A random sample of 64 employees is taken. What is the likelihood that the sample mean will be 26 hours or less?
Probabilistic Likelihood 

PROBLEM 3 (60 points) :
The average grade point average (GPA) of undergraduate students in New York is normally distributed with a population mean of 2.5 and a population standard deviation of .5. Compute the following, showing all work:
(I) The percentage of students with GPA's between 1.3 and 1.8 is: (a) less than 5.6%
(b) 5.7% (c) 5.9% (d) 6.2% (e) 6.3% (f) 6.6% (g) 7.3% (h) 7.5%
i) 7.9% (j) more than 8%.
Choice 

(II) The percentage of students with GPA's above 3.4 is:
Percentage 

(III) Above what GPA will the top 5% of the students be (i.e., compute the 95th percentile):
GPA 

(IV) If a sample of 25 students is taken, what is the probability that the sample mean GPA will be between 2.50 and 2.75? (a) less than .10 (b) .122 (c) .243 (d) .307 (e) .346
(f) .38 (g) .42 (h) .44 (i) .494 (j) more than .494.
Choice 

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