Statistics
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: Composers Percentage of Requests Bach 5 Beethoven 26 Brahms 9 Dvorak 2 Mendelssohn 3 Mozart 21 Schubert 12 Schumann 7 Tchaikovsky 14 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 Probation 2.5 - < 3.0 3.0 - < 3.5 3.5 and above Total
Yes
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 Probation 2.5 - < 3.0 3.0 - < 3.5 3.5 and above Total
Yes