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Assignment 2 - Applied Statistics Stats I: hand in your own (!) work on
A political researcher tries to find out how large the support for the Gambian president is,
who claims at least half of the voters support him. The researchers interviews 400 (arbitrary
chosen) voters all over the country and guarantees total confidentiality. X is the number of
supporters among the 400 voters.
a. What distribution does X have (name an exact distribution and an approximating
distribution, including the parameters)?
b. If the claim of the president is just right (50% support), compute the probability that the
researcher finds that 48% or less of the voters in his sample are supporting the president.
c. What is the distribution of
?
The scores of an IQ-test of students of UTG are (approximately ) normally distributed with
expectation 110 and standard deviation 12.
d. What is the probability that an arbitrary UTG-student has an IQ-score higher than 115?
e. Find the top 10% of IQ-scores of UTG-students.
f. If a group of 25 UTG-students are tested, find the distribution of the mean IQ-score and
the probability that the mean IQ-score is higher than 115.
Solution assignment 2 AS
a. X is B(400, p) (p is the unknown proportion of supporters among voters)
X is approximately N( 400p, 400p(1-p) )
b. For p = ½ , X is approximately N( 200, 100 )
48% of 400 is 192: P(X ≤ 192) = P(X ≤ 192.5) =
c.
is approximately N(p,
d. P(X > 115) =
e. P(X ≥ t ) = 0.1 => P(X ≤ t ) = 0.9 =>
f.
) = N(0.5, 1/1600)
1-0.6648 = 33.52%
0.90 =>
is N(µ, σ2/n)-distributed =>
= 1.88%
Marks:
a b c d e f Total
2 2 1 1 2 2
10
=> t ≈125