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 70% 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.)

If this actually happened, might it shake your confidence in the statement p = 0.70? Might it make you suspect that p is less than 0.70? Explain.

No. A probability this small might indicate that the true value of p is less than 0.70.

Yes. A probability this small might indicate that the true value of p is greater than 0.70.

No. A probability this small might indicate that the true value of p is greater than 0.70.

Yes. A probability this small might indicate that the true value of p is less than 0.70.

(e) More than 17 out of the next 20 business days. (Use 3 decimal places.)

If this actually happened, might you suspect that p is greater than 0.70? Explain.

No. This is unlikely to happen if the true value of p is 0.70.

Yes. This is likely to happen if the true value of p is 0.70.

Yes. This is unlikely to happen if the true value of p is 0.70.

No. This is likely to happen if the true value of p is 0.70.

Answer 1

(a)

Let X is a random variable shows the number of days store will gross over $850 out of 5 business day.

Here X has binomial distribution with parameters n=5 and p=0.70.

Therefore, the probability that that the store will gross over $850 at least 3 out of 5 business days is

Answer: 0.837

(b)

Let X is a random variable shows the number of days store will gross over $850 out of 10 business day.

The random variable X has binomial distribution with parameters n=10 and p=0.70.

The probability that that the store will gross over $850 at least 6 out of 10 business days is

Answer: 0.850

(c)

The probability that that the store will gross over $850 fewer than 5 out of 10 business days is

Answer: 0.047

(d)

Let X is a random variable shows the number of days store will gross over $850 out of 20 business day.

X has binomial distribution with parameters n=20 and p=0.70.

The probability that that the store will gross over $850 fewer than 6 out of the next 20 business days is

Answer: 0.000

Yes. A probability this small might indicate that the true value of p is less than 0.70.

(e)

Answer: 0.035

Yes. This is unlikely to happen if the true value of p is 0.70.