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Question
USA Today reported that 11% of all books sold are of the romance genre. If a local bookstore sells 316 books on a given day, what is the probability that
a) fewer than 40 are romance?
b) at least 25 are romances?
c) between 25 and 40 are romances?
d) In the solution to this problem, What is n? p? q? Does it appear that both np and nq are larger than 5? Why is this an important consideration?
Submitted: 316 days and 13 hours ago.
Category: Math
Value: $9
Status: CLOSED
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Optional Information
Subject: statistics
Accepted Answer
n = 316
p = 0.11
q = 1 - p = 1 - 0.11 = 0.89
np = 316*0.11 = 34.76
In all questions we use the
continuity correction
.
(A)
P(X < 40) = P(X ≤ 39) = P(Z < (39.5-34.76)/√(34.76(1-0.11))) = P(Z < 0.85) = 0.8023
(B)
P(X ≥ 25) = P(Z > (24.5-34.76)/√(34.76(1-0.11))) = P(Z > -1.845) = 0.9675
(C)
P(25 ≤ X ≤ 40) = P((24.5-34.76)/√(34.76(1-0.11)) < Z < (40.5-34.76)/√(34.76(1-0.11))) = P(-1.845 < Z < 1.03) = 0.816
(D)
np = 34.76
nq = 316*0.89 = 281.24
both are larger than 5, this is important for assuring a good normal approximation.
Sincerely,
Sk1llz
Expert:
Sk1llz
Pos. Feedback:
100.0 %
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Answered:
1/10/2009
Mastermind
Mathematics, Statistics and Physics
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