Homework Sourse1 57 of men consider themselves professional baseball fans Y
1. 57% of men consider themselves professional baseball fans. You randomly select 10 men and ask if each considers himself a professional baseball fan. Find the probability that the number who considers themselves baseball fans is (a) exactly 8, (b) at least 8, and (c) less than 8. If conveint, use technology to find the probabilities.
2. 45% of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in saving. Find the probability that the number that they say would feel secure is (a)exactly five, (b) more than 5, (C) at most 5.
3.
Solution
1.
a)
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 10
p = the probability of a success = 0.57
x = the number of successes = 8
Thus, the probability is
P ( 8 ) = 0.09271463 [answer]
b)
Note that P(at least x) = 1 - P(at most x - 1).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 10
p = the probability of a success = 0.57
x = our critical value of successes = 8
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 7 ) = 0.87635375
Thus, the probability of at least 8 successes is
P(at least 8 ) = 0.12364625 [answer]
c)
Note that P(fewer than x) = P(at most x - 1).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 10
p = the probability of a success = 0.57
x = our critical value of successes = 8
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 7 ) = 0.87635375
Which is also
P(fewer than 8 ) = 0.87635375 [answer]
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