# Statistics

Topics: Standard deviation, Arithmetic mean, Skewness Pages: 7 (1540 words) Published: November 4, 2011
1. A radio station that plays classical music has a “By Request” program each Saturday night. The percentage of requests for composers on a particular night are listed below: ComposersPercentage of Requests

Bach 5
Beethoven26
Brahms 9
Dvorak 2
Mendelssohn 3
Mozart21
Schubert12
Schumann 7
Tchaikovsky14
Wagner 1

a. Does the data listed above comprise a valid probability distribution? Explain.

The individual probabilities are all between 0 & 1 and the sum = 100%

b. What is the probability that a randomly selected request is for one of the three B’s?

P(one of the B’s) = P(Bach) + P(Beethoven) + P(Brahms) = 5 + 26 + 9 = 40%

c. What is the probability that a randomly selected request is for a Mozart piece?

P(Mozart) = 21%

d. What is the probability that a randomly selected request is not for one of the two S’s?

P(not Schubert or Schumann) = 1 – P(Schubert or Schumann) = 1 – (12 + 7)
= 81%

e. Neither Bach nor Wagner wrote any symphonies. What is the probability that a randomly selected request is for a composer who wrote at least one symphony?

P(Symphony) = 1 – P(Bach or Wagner)
= 1 – (5 + 1)
= 94%

f. What is the probability that a randomly selected request is for a composer other than one of the three B’s or one of the two S’s?

P( not a B or not a S) = P(Dvorak, Mendelssohn, Mozart, Tchaikovsky, or Wagner)
= (2 + 3 + 21 + 14 + 1)
= 41%

2. Five hundred first-year students at a state university were classified both according to high school GPA and whether or not they were on academic probation at the end of their first semester.

High School GPA
Probation2.5 - < 3.03.0 - < 3.53.5 and aboveTotal

Yes 50 55 30 135

No 45 135 185 365

Total 95 190 215 500

Use the table to determine the probability that a randomly selected first-year student will be on academic probation at the end of the first semester.
P ( on academic probation) = 135/500 = 0.27

What is the probability that a randomly selected first-year student had a GPA of 3.5 or above? P (GPA >= 3.5) = 215/500 = 0.43

Are the outcomes selected student has a GPA of 3.5 or above and selected student is on academic probation at the end of first semester independent? How can you tell? For the events to be independent, P (GPA >= 3.5) must equal P (GPA >= 3.5 given the student is on probation)

P (GPA >= 3.5) = 0.43 and
P (GPA >= 3.5 given the student is on probation) = 30/135 = 0.22 The probabilities are not equal therefore, the events are not independent.

What is the probability that a first-year student will have a high school GPA of between 2.5 and 3.0 and will also be on academic probation at the end of the first semester of college? P (2.5 < GPA < 3.0 and on academic probation) = 50/500 = 0.10

What is the probability that a first year student will have a high school GPA of 3.5 or above and will not be on probation at the end of first semester of college? P (GPA >= 3.5 and not on academic probation) = 185/500 = 0.37

3. For several years, evidence has been mounting that folic acid reduces major birth defects. An issue of The Arizona Republic reported on a Hungarian study that provides the strongest evidence yet.  The results of the study, directed by Dr. Andrew E. Czeizel and Dr. Istvan Dudas of the National Institute of Hygiene in Budapest, were published in The New England Journal of Medicine.  For the study, the doctors enrolled 4753 women prior to conception. The women were...