There are four auto body shops in Bangor, Maine, and all claim to promptly repair cars. To check if there is any difference in repair times, customers are randomly selected from each repair shop and their repair times in days are recorded. The output from a statistical software package is: Is there evidence to suggest a difference in the mean waiting times at the four body shops? Use the 0.05 significance level. Compute the critical value. (Round your answer to 2 decimal places.) State the decision regarding the null hypothesis.

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Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?