Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove Creek, Montana. After examining accounting records for 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 probability that the store will gross over $850 for the following.(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 of the next 20 business daysIf the outcome described in part (d) actually occurred, might it shake your confidence in the statement p = 0.70? Might it make you suspect that p is less than 0.70? Explain.(e)more than 17 out of the next 20 business daysIf the outcome described in part (e) actually occurred, might you suspect that p is greater than 0.70? Explain.Step 1(a)at least 3 out of 5 business daysFirst, we must determine that this is a binomial experiment. To do so, check the 5 requirements:There is a fixed number of trials, n. Yes, n =

The outcomes of each trial are independent. Yes, the grossing of the store each day does not affect the grossing of the store on other days. Each trial can result in just two possible outcomes. We define one outcome to be a "success" and the other outcome to be a "failure". Yes, the store either grosses over $850 (success) or it does not (failure). The probability of a success, denoted by p, remains the same from trial to trial. Yes, the probability of grossing over$850 is given as 70% or 0.70. The random variable Y = the number of successes.

Now, we can use the binomial probability formula to calculate the probability of getting at least 3 successes in 5 trials.

P(Y >= 3) = P(Y = 3) + P(Y = 4) + P(Y = 5)

We can calculate each of these probabilities using the binomial probability formula:

P(Y = k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where C(n, k) is the number of combinations of n items taken k at a time, p is the probability of success, and n is the number of trials.

So,

P(Y = 3) = C(5, 3) * (0.70^3) * ((1-0.70)^(5-3)) P(Y = 4) = C(5, 4) * (0.70^4) * ((1-0.70)^(5-4)) P(Y = 5) = C(5, 5) * (0.70^5) * ((1-0.70)^(5-5))

Add these probabilities together to get P(Y >= 3).

Repeat these steps for parts (b), (c), (d), and (e), adjusting the values of n and k as necessary.

For part (d), if the outcome actually occurred, it might shake your confidence in the statement p = 0.70, as it would suggest that the probability of grossing over $850 is less than 70%.

For part (e), if the outcome actually occurred, it might make you suspect that p is greater than 0.70, as it would suggest that the probability of grossing over $850 is more than 70%.