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True/False Questions: Given a binomial random variable X with n=5 and p=.4, then

ID: 3021717 • Letter: T

Question

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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