SOLUTION: 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 bin

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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.
b) What is the mean number (expected value) of left-handers in the class?
c) What is the probability that there is exactly 5 left-handers in the class?
d) What is the probability that the number of left-handers are between 6 and 10 inclusively (including 6 and 10)?
Answer by reviewermath(1029) About Me  (Show Source):
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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.
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%284%29
c) What is the probability that there is exactly 5 left-handers in the class?
P%28X+=+5%29+=+%28matrix%282%2C1%2C20%2C5%29%29%280.2%5E5%29%280.8%5E15%29 = highlight%280.17456%29
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%28%28matrix%282%2C1%2C20%2Cx%29%29%280.2%5Ex%29%280.8%5E%2820-x%29%29%2Cx+=+6%2C10%29 = highlight%280.19523%29