The average value is given by
Setting
, you get 
, and the integral becomes
Setting
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Answer:
Probability that the sample contains at least five Roman Catholics = 0.995 .
Step-by-step explanation:
We are given that In Quebec, 90 percent of the population subscribes to the Roman Catholic religion.
The Binomial distribution probability is given by;
P(X = r) = for x = 0,1,2,3,.......
Here, n = number of trials which is 8 in our case
r = no. of success which is at least 5 in our case
p = probability of success which is probability of Roman Catholic of
0.90 in our case
So, P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)
=
= 56 * + 28 *
+ 8 *
+ 1 *
= 0.995
Therefore, probability that the sample contains at least five Roman Catholics is 0.995.