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Answer:
a. 0.9931
b. 0.3423
c. 0.3907
d. 0.2670
e. 3.15
f. 1.0796
Step-by-step explanation:
The probability of the variable that said the number of left-handed people follow a Binomial distribution, so the probability is:
nCx is calculated as:
Where x is the number of left-handed people, n is the number of people selected at random and p is the probability that a person is left--handed. So P(x) is:
Then the probabilities P(0), P(1), P(2), P(3), P(4) and P(5) are:
Then, the probability P(x≥1) that there are some lefties among the 5 people is:
P(x≥1) = P(1) + P(2) + P(3) + P(4) + P(5)
P(x≥1) = 0.0590 + 0.2011 + 0.3423 + 0.2914 + 0.0993 = 0.9931
The probability P(3) that there are exactly 3 lefties in the group is:
P(3) = 0.3423
The probability P(x≥4) that there are at least 4 lefties in the group is:
P(x≥4) = P(4) + P(5) = 0.2914 + 0.0993 = 0.3907
The probability P(x≤2) that there are no more than 2 lefties in the group is:
P(x≤2) = P(0) + P(1) + P(2) = 0.0069 + 0.0590 + 0.2011 = 0.2670
On the other hand, the expected value E(x) and standard deviation S(x) of the variable that follows a binomial distribution is: