Question

According to a recent study, only 41% of auto mechanics correctly diagnose a common vehicle problem. 9 auto mechanics are randomly selected and then each is tested to see if she/he correctly diagnoses the vehicle problem. Use this situation to answer the parts below.

(a) Recognizing that this is a binomial situation, give the meaning of S & F in this context. Define what you will classify as success and failures.

(b) Next, give the values of n, p, and q

(c) Construct the complete binomial probability distribution table for this situation at the right

(d) Using your table, find the probability that exactly six of nine randomly selected mechanics diagnose the common vehicle problem correctly.

(e) Find the probability that at least four of the nine diagnose correctly

(f) Find the probability that less than two of the nine will misdiagnose the problem

(g) Find the mean and standard deviation of this binomial probability distribution

(h) By writing a sentence, interpret the meaning of the mean value found in (g) as tied to the context of mechanics diagnoses of vehicle problem

(i) Is it unusual to have all nine of randomly selected auto mechanics correctly diagnose vehicle problem? Briefly explain your answer giving supporting numerical evidence.

Answer 1