A recent CBS News survey reported that 61% of adults felt the U.S. Treasury shou
ID: 3442744 • Letter: A
Question
A recent CBS News survey reported that 61% of adults felt the U.S. Treasury should continue making pennies.
How many of the 15 would we expect to indicate that the Treasury should continue making pennies?(Round your answer to 2 decimal places.)
What is the standard deviation? (Round your answer to 4 decimal places.)
What is the likelihood that exactly 8 adults would indicate the Treasury should continue making pennies? (Round your answer to 4 decimal places.)
What is the likelihood at least 8 adults would indicate the Treasury should continue making pennies?(Round your answer to 4 decimal places.)
A recent CBS News survey reported that 61% of adults felt the U.S. Treasury should continue making pennies.
Explanation / Answer
a-1.
mean = n p = 15*0.61 = 9.15 [answer]
****************
a-2.
standard deviation = sqrt(n p (1-p)) = sqrt(15*0.61*(1-0.61)) = 1.889047379 [answer]
******************
b)
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 = 15
p = the probability of a success = 0.61
x = the number of successes = 8
Thus, the probability is
P ( 8 ) = 0.169293187 [answer]
*******************
c)
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 = 15
p = the probability of a success = 0.61
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 ) = 0.19019142
Thus, the probability of at least 8 successes is
P(at least 8 ) = 0.80980858 [ANSWER]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.