A recent CBS News survey reported that 61 of adults felt the

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.)

Solution

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]