The probability that:
a.  A score is greater than 1.5.
b.  A score is less than -1.8.
c.  A score is between -1.5 and 1.5.
d.  A score is between -1.8 and 1.5.
e.  A score is between  1.5 and 1.8.
The score that:
f.  Has 10% of the distribution above it.
g.  Has 20% of the distribution below it.
The pair of symmetric scores that:
h.  Have 90% of the distribution between them.


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2.  A pool of 1000 applicants to a certain college has mean SAT
score of 650.  Their standard deviation is 25.
a.  What is the probability that an applicant chosen at random
will have a score greater than 680?
b.  How many applicants will have scores greater than 710?
c.  How many will have scores between 630 and 640?
d.  What score has 10% of the scores below it?


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3.  Consider the applicant pool in problem two to be a
population.
  
a.  Draw a sample of 25 students.  What is the standard error of
the mean?


b.  Suppose the sample mean equals 677.  Put a 95% confidence
bound around it.
   
c.  Draw a sample of 100 students.  What is the standard error of
the mean?

d.  Assume the sample mean also equals 677.  Put a 95% confidence
bound around it.

e.  Complete parts a through d if the population standard
deviation equals 50 instead of 25.

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4a.  For the samples and standard deviations in problem three
test the hypothesis that a sample mean of 657 does not equal
the population mean of 650.


b.  For the samples and standard deviations in problem three test
the hypothesis that a sample mean of 657 is greater than the
population mean of 650.


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5a.  Suppose hospital length of stay for hysterectomy has
historically been six days with a standard deviation of two days.

A hospital administrator wants to determine if a new management
policy can lower this mean to 5.5 days.  Compute sample size
requirements for the following situations.

              alpha              power
              one sided .05       .8
              two sided .05       .8
              one sided .05       .9
              one sided .01       .9


b.  Repeat part a assuming the population standard deviation
equals three days.

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