True/False Questions: Given a binomial random variable X with n=5 and p=.4, then
ID: 3021717 • Letter: T
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True/False Questions: Given a binomial random variable X with n=5 and p=.4, then P(X is at least 2) is .317? Given a binomial random variable X with n=10 and p=.75, the probability that X=5 is.058? The variance of a data set could be smaller than its standard deviation? Suzy and Fran toss a coin over cab fare. The probability that Suzy will pay five days in a row is .03125? The sum of the mean deviations in a data set always = 0? In a sample of 25 with standard deviation 4 the sum of squared deviations from the sample mean is 96? Two events A and B are independent if P(AandB)=P(A)xP(B)? If R and S are independent events with P(R) =.30 and P(S)=.50, then P(RorS)=.65? True/False Questions: Given a binomial random variable X with n=5 and p=.4, then P(X is at least 2) is .317? Given a binomial random variable X with n=10 and p=.75, the probability that X=5 is.058? The variance of a data set could be smaller than its standard deviation? Suzy and Fran toss a coin over cab fare. The probability that Suzy will pay five days in a row is .03125? The sum of the mean deviations in a data set always = 0? In a sample of 25 with standard deviation 4 the sum of squared deviations from the sample mean is 96? Two events A and B are independent if P(AandB)=P(A)xP(B)? If R and S are independent events with P(R) =.30 and P(S)=.50, then P(RorS)=.65? Given a binomial random variable X with n=5 and p=.4, then P(X is at least 2) is .317? Given a binomial random variable X with n=10 and p=.75, the probability that X=5 is.058? The variance of a data set could be smaller than its standard deviation? Suzy and Fran toss a coin over cab fare. The probability that Suzy will pay five days in a row is .03125? The sum of the mean deviations in a data set always = 0? In a sample of 25 with standard deviation 4 the sum of squared deviations from the sample mean is 96? Two events A and B are independent if P(AandB)=P(A)xP(B)? If R and S are independent events with P(R) =.30 and P(S)=.50, then P(RorS)=.65?Explanation / Answer
Given a binomial random variable X with n=5 and p=.4, then P(X is at least 2) is .317?
[ANSWER, FALSE]
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 = 5
p = the probability of a success = 0.4
x = our critical value of successes = 2
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 1 ) = 0.33696
Thus, the probability of at least 2 successes is
P(at least 2 ) = 0.66304 [FALSE]
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Given a binomial random variable X with n=10 and p=.75, the probability that X=5 is.058?
[ANSWER, TRUE]
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 = 0.75
x = the number of successes = 5
Thus, the probability is
P ( 5 ) = 0.0583992 [TRUE]
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The variance of a data set could be smaller than its standard deviation?
TRUE. [This can happen if the variance is less than 1.]
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