25% of netflix customers watch movies online from netflix catalog. assuming a binomial distribution, if a sample of 10 customers is selected, what is the probability that 3 or more but not greater than 7 watch movies online. expert ans

Step-by-step explanation:

Let's define X = amount of customers that watch movies online. X has a binomial distribution with the probability of watching a movie online in a sample of 10 customers (we notate it as X B (10,), 10 and are the parameters of X).

Let's remember that the probability of getting exactly k successes (i.e. k customers that watch movies online) in n trials (n is the total of the sample), in a binomial distribution X with parameters (n, p), is given by the probability mass function:  

In our exercise, we need 3 or more but not greater than 7 successes. That means, we need to find out .  

Let's notice that this is equal to have 3, 4, 5, 6 or 7 customers that watch movies online.

So,

Now we just use the probability mass function, with n=10 and p=1/4, for each k ⊆ {3, 4, 5, 6, 7}:

Now we just do the calculation and we get

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