Thirty percent of all customers who enter a store will make

Thirty percent of all customers who enter a store will make a purchase. Suppose that six customers enter the store and that these customers make independent purchase decisions.

Use the binomial formula to calculate the probability that exactly five customers make a purchase. (Round your answer to 4 decimal places.)

Use the binomial formula to calculate the probability that at least three customers make a purchase. (Round your answer to 4 decimal places.)

Use the binomial formula to calculate the probability that two or fewer customers make a purchase. (Round your answer to 4 decimal places.)

Use the binomial formula to calculate the probability that at least one customer makes a purchase. (Round your answer to 4 decimal places.)

Solution

1.

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 =    6      
p = the probability of a success =    0.3      
x = the number of successes =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.010206 [ANSWER]

*****************

Consider:

2.

          
Thus, the probability of at least   3   successes is  
          
P(at least   3   ) = P(3) + P(4) + P(5) + P(6) = 0.25569 [ANSWER]

*******************

3.

          
Then the cumulative probability is          
          
P(at most   2   ) = P(0) + P(1) + P(2) = 0.74431 [ANSWER]

********************

4.

Thus, P(at least one) = 1 - P(0) =   0.882351 [ANSWER]