A large company is reviewing the workplace accident data for the last year. They would like to test the null hyposthesis that accidents are eqaully likely to occur on each weekday (i. e. the null hypothesis is that20% of accidents occur on Monday, 20% occur on Tuesday, 20% occur on Wednesday, 20% occur on Thursday and 20% occur on Friday). Over the last year, there have been 127 accidents. Determine the number of accidents expected to occur on Mondays. Give your answer to 1 decimal place.

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?