at a local restaurant 45% of the customers order spaghetti. Estimate the probability that 6 of the next 10 customers will order spaghetti.

P(6) = (0.45)^6*(0.55)^4*10!/(6!*4!) = 210*(8.304*10^-3)*(9.151*10^-2) = 0.1596

P(4) and P(5) will be higher, since the average number of spaghetti eaters out of 10 will be 4.5

To estimate the probability that exactly 6 out of the next 10 customers will order spaghetti, we can use the binomial probability formula.

The binomial probability formula is:
P(x) = (nCx) * (p^x) * ((1-p)^(n-x))

Where:
P(x) is the probability of getting exactly x successes,
n is the total number of trials or customers (in this case, 10),
x is the number of successful events (in this case, 6),
p is the probability of success in a single trial (in this case, 45% or 0.45),
1-p is the probability of failure in a single trial.

Now, let's calculate the probability:

P(6) = (10C6) * (0.45^6) * (0.55^4)

(10C6) means the number of combinations of choosing 6 out of 10 customers. This can be calculated as:
(10C6) = 10! / (6! * (10-6)!)

Let's calculate each part step-by-step:

(10C6) = 10! / (6! * 4!)
= (10 * 9 * 8 * 7 * 6!) / (6! * 4!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2)
= 210

Now, let's substitute the values into the formula:

P(6) = 210 * (0.45^6) * (0.55^4)
≈ 0.210 * 0.0084 * 0.0915
≈ 0.001467

Therefore, the estimated probability that exactly 6 out of the next 10 customers will order spaghetti is approximately 0.001467, or 0.1467%.