In a study 1 examining gender bias, a nationwide sample of 127 science professors evaluated the application materials of an undergraduate student who had ostensibly applied for a laboratory manager position. all the faculty members received the same application, with half randomly given a male name and half randomly given a female name. we see that the applications with female names received a significantly lower recommended salary. does gender of the evaluator make a difference? in particular, considering only the 64 applications with female names, is the mean recommended salary different depending on the gender of the evaluating faculty member? the 32 male faculty gave a mean starting salary of $27,111 with a standard deviation of $6,948 while the 32 female faculty gave a mean starting salary of $25,000 with a standard deviation of $7,966. the standard error of the difference is $1,868.14.

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?