If 90 of automobiles in a county have both headlights workin

If 90% of automobiles in a county have both headlights working.

a. What is the probability that in a sample of 10 automobiles, at least 7 will have both headlights working?

b. IN a sample of 100 cars, how many cars do you expect to see with both headlights working?

PLEASE ANSWER BOTH PARTS SHOWING ALL EQUATIONS USED OR I WILL NOT THUMBS UP! THANKS!

Solution

A)

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 =    10      
p = the probability of a success =    0.9      
x = our critical value of successes =    7      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   6   ) =    0.012795198
          
Thus, the probability of at least   7   successes is  
          
P(at least   7   ) =    0.987204802 [ANSWER]

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b)

Expected value = n p = 100*0.90 = 90 CARS [ANSWER]