Trevor is interested in purchasing the local hardware/sporting goods store in th

Question

Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove Creek, Montana. After examining accounting records or the past several years, he found that the store has been grossing over $850 per day about 69% of the business days it is open. Estimate the following probabilities that the store will gross over $850. (a) At least 3 out of 5 business days. (Use 3 decimal places.) (b) At least 6 out of 10 business days. (Use 3 decimal places.) (c) Fewer than 5 out of 10 business days. (Use 3 decimal places.) (d) Fewer than 6 out of the next 20 business days. (Use 3 decimal places.)

Explanation / Answer

Solution

Let X = number of days out of n business days when store grosses over $850 per day.

Then, X is Binomially distributed with parameters n and p, where p = probability of grossing over $850 per day. Given, the store has been grossing over $850 per day about 69% of the business days it is open, p = 0.69.

(a) We want P(X 3) when n = 5. From Standard Binomial Probability Tables,

P(X 2) = 0.1766 => P(X 3) = 1 – 0.1766 = 0.823 ANSWER   

(b) We want P(X 6) when n = 10. From Standard Binomial Probability Tables,

P(X 5) = 0.1679 => P(X 6) = 1 – 0.1679 = 0.832 ANSWER

(c) We want P(X 4) when n = 10. From Standard Binomial Probability Tables,

P(X 4) = 0.0551 = 0.055 ANSWER   

(d) We want P(X 5) when n = 20. From Standard Binomial Probability Tables,

P(X 5) = 0.000 ANSWER[the probability has first significant digit at the 5th position]

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.