According to a survey, 20% of the car owners said that they get the maintenance

Question

According to a survey, 20% of the car owners said that they get the maintenance service done on their cars according to the schedule recommended by the auto company. Suppose that this result is true for the current population of car owners. a. Let x be a binomial random variable that denotes the number of car owners in a random sample of 12 who get the maintenance service done on their cars according to the schedule recommended by the auto company. What are the possible values that x can assume? Integers to . b. Find to 3 decimal places the probability that exactly 4 car owners in a random sample of 12 get the maintenance service done on their cars according to the schedule recommended by the auto company. Use the binomial probability distribution formula. Probability =

Explanation / Answer

X can assume all values from 0 to 12 in the sample of 12

Binomial probabilty formula is given as

P(x=4) = 12C4 * p(4) * q (12-4) where p = 0.2 and q = 1-p = 0.8

P(x=4) = 12*11*10*9 *( 0.2^4) * 0.8^8 / ( 1*2*3*4) = 0.1328

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