According to a recent study, only 41% of auto mechanics correctly diagnose a common vehicle problem. Nine 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 S and F in this context. That is, define what you will classify as a "success" and what you will classify as a "failure" when one adult is selected and tested for a common vehicle problem.
S =
F =
(b) Next, give the values of n, p, and q. (Here q is the complement of p: q = 1− p.)
n = p = q =
(c) Construct the complete binomial probability distribution table for this situation at the right. x P(x)
(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.
0
(f) Find the probability that less than two of the nine will misdiagnose the problem.
0
(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 correctly diagnosing a problem.
(i) Is it unusual to have all nine mechanics correctly diagnose the problem? Briefly explain your answer giving supporting numerical evidence. (Hint: might use the 2 Sigma Rule)