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Statistics - Binomial Probabilities

Trevor is interested in purchasing the local hardware/sporting goods in the small town of Dove creek, Montana. After examing accounting records for the past several years, he found that the store has been grossing over $850 per day about 60% of the business days it is open. Estimate the probability that the store will gross over $850

a. at least 3 out of 5 business days

b. at least 6 out of 10 business days

c. fewer than 5 out of 10 business days

d. fewer than 6 out the next 20 business days. If this actually happened, might it shake your confidence in the statement p = 0.60? Might it make you suspect that p is less than 0.60? Explain.

e.more than 17 out of the next 20 business days. If this actually happened, might you suspect that p is greater than 0.60. Explain.

Solution Preview

p = 0.6, q = 1 - p = 0.4; P(r successes in n trials) = nCr p^r q^(n - r)

(a) P(At least 3 out of 5 days) = P(3) + P(4) + P(5)

= 5C3 0.6^3 0.4^2 + 5C4 0.6^4 0.4^1 + 5C5 0.6^5 0.4^0

= 0.6826

(b) P(At least 6 out of 10 ...

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