According to the Yankee Group, 60% of all cable households rate cable companies

Question

According to the Yankee Group, 60% of all cable households rate cable companies as good or excellent in having professional personnel. Suppose 300 cable households are randomly contacted. Use Normal approximation to binomial problems to answer the following question: What is the probability that between 155 and 170 (inclusive), i.e. P(155 x 170), cable households rate cable companies as good or excellent in having professional personnel?

0.3686

0.4987

0.8673

0.1301

0.1327

0.3686

0.4987

0.8673

0.1301

0.1327

Explanation / Answer

Probability of success, p = 0.6, mean= n*p = 300*0.6 = 180, std. dev. = sqrt(n*p*q) = 8.485281

P(155 <= x <= 170) = P(X <= 170) - P(X <= 155) = P(X < 170.5) - P(X < 155.5)
= P(Z < (170.5 - 180)/8.485281) - P(Z < (155.5 - 180)/8.485281) = P(Z < -1.1196) - P(Z < -2.8874)
= 0.1314 - 0.0019 = 0.1295

Answer: Option D 0.1301
(The difference is due to the precision used in calculation)

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