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joy3449
29.07.2019 •
Mathematics
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
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Ответ:
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,![P(3\leq X\leq 7) = P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7)](/tpl/images/0147/2675/abe7a.png)
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
Ответ:
-5.2
Let me know if this helps!