in a certain state about 70 of drivers whoe are arrested for

in a certain state, about 70% of drivers whoe are arrested for driving while intoxicated are convicted.

if 12 independently selected drivers were arrested for dwi how many would be convicted?

6, 8 , 7, 9

what is the probabilikty that exactly 8 out of 12 would be convicted

what is probablitiy that 8 or fewer would be convicted?

Solution

A)

if 12 independently selected drivers were arrested for dwi how many would be convicted?

As

u (mean) = n p

Then

u = 12*0.7 = 8.4. [ANSWER, 8 (rounded to the nearest integer)]

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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 =    12      
p = the probability of a success =    0.7      
x = the number of successes =    8      
          
Thus, the probability is          
          
P (    8   ) =    0.231139696 [ANSWER]

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C)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    12      
p = the probability of a success =    0.7      
x = the maximum number of successes =    8      
          
Then the cumulative probability is          
          
P(at most   8   ) =    0.507484227 [ANSWER]