Trevor is interested in purchasing the local hardware/electronic goods store in a small town in South Ohio. After examining 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

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Trevor is interested in purchasing the local hardware/electronic goods store in a small town in South Ohio. After examining 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 at least 6 out of 10 business day

P( at least 6 out of 10 business days ) = 0.6312

Step-by-step explanation:

Given the data in the question;

p = 60% = 0.6

q = 1 - p = 1 - 0.6 = 0.4

Using Binomial distribution;

P( X = r ) =

where

we substitute

P( at leas 6 ) = P(6) + P(7) + P(8) + P(9) + P(10)

= [¹⁰C₆ × 0.6⁶ × 0.4⁴] + [¹⁰C₇ × 0.6⁷ × 0.4³] + [¹⁰C₈ × 0.6⁸ × 0.4²] + [¹⁰C₉ × 0.6⁹ × 0.4¹] + [¹⁰C₁₀ × 0.6¹⁰ × 0.4⁰]

= [0.250] + [0.214] + [0.1209] + [ 0.0403] + [ 0.00604 ]

= 0.6312

Therefore, P( at least 6 out of 10 business days ) = 0.6312

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step-by-step explanation: