Need help please

Question

At Starbucks customers can choose the drinks among three sizes: Tall, Grande, Venti. Suppose of all customers, 36% chooses Tall, 26% chooses Grande, and 38% (the rest) choose Venti. On one afternoon, 11 customers came to the store. What is the probability that between 5 to 7 customers (inclusively, so between 4.5 - 7.5 I think) choose Grande size?

Also,

What is the probability that that at most 3 customers choose Tall size?

Answer 1

Cannot use normal approximation to binomial distribution because insufficient sample size.

So use binomial formula for p = 0.26 (Grande), n = 11 and x = 5, 6 and 7, summing probabilities for the three values of x

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

For second part, use binomial formula for x = 0, 1, 2 and 3, sum probabilities, then subtract from 1.