Question 767788
The probability that an individual is left-handed is .20. Let the random variable X bethe number of left-handers in a class of 20 students. Assuming the random variable X has a binomial distribution:
a) What is the probability distribution, P(X) of the random variable X.
{{{highlight(P(X = x) = (matrix(2,1,20,x))(0.2^x)(0.8^(20-x)))}}} for x = 0,1,2,...,20
b) What is the mean number (expected value) of left-handers in the class?
Mean, E(X) = np = 20(0.2) = {{{highlight(4)}}}

c) What is the probability that there is exactly 5 left-handers in the class?
{{{P(X = 5) = (matrix(2,1,20,5))(0.2^5)(0.8^15)}}} = {{{highlight(0.17456)}}}
d) What is the probability that the number of left-handers are between 6 and 10 inclusively (including 6 and 10)?
P(6 ≤ X ≤ 10) = {{{sum((matrix(2,1,20,x))(0.2^x)(0.8^(20-x)),x = 6,10)}}} = {{{highlight(0.19523)}}}