One year Thomas had the lowest ERA​ (earned-run average, mean number of runs yielded per nine innings​ pitched) of any male pitcher at his​ school, with an ERA of 3.26. ​Also, Karen had the lowest ERA of any female pitcher at the school with an ERA of 3.17. For the​ males, the mean ERA was 4.286 and the standard deviation was 0.567. For the​ females, the mean ERA was 4.022 and the standard deviation was 0.873.   Find their respective​ z-scores. Which player had the better year relative to their​ peers, Thomas or Karen​? ​(Note: In​ general, the lower the​ ERA, the better the​ pitcher.)   Thomas had an ERA with a​ z-score of ____________. Karen had an ERA with a​ z-score of __________. ​(Round to two decimal places as​ needed.)   Which player had a better year in comparison with their​ peers?   A. Thomas had a better year because of a lower​ z-score.   B. Karen had a better year because of a higher​ z-score.   C. Thomas had a better year because of a higher​ z-score.   D. Karen had a better year because of a lower​ z-score.

The census bureau reported that the mean household income in Hayward in 2019 was $86,744 with a standard deviation of $18,700. A simple random sample of 150 households from Hayward had a mean income of $89,396 with a standard deviation of $23,156. Find the probability that a sample of this size will indicate a mean of $89,396 or more?

The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a random sample of 75 Buffalo residents the mean is 25 miles a day. The standard deviation of the population (Buffalo residents) is 5.1 miles a day. For an independent random sample of 60 Boston residents the mean is 23 miles a day. The standard deviation of the population (Boston residents) is 8.2 miles a day. Consider the following hypothesis test. Mean 1 = Buffalo residents ; Mean 2 = Boston Residents Ho : 1 – H2 = 0 H : H1 - 42 0 At alpha = 0.05 what is your conclusion? 0.05 -3.6 0002 0002 0001 0001 .0001 .0001 000 0001 .0001 0001 0.01 0.02 0.04 0.06 0.07 0.09 0.00 0.03 0.08 -3.5 .0002 0002 .0002 0002 .0002 .0002 0002 .0002 .0002 0002 -3.4 0003 .0003 .0003 0003 .0003 0003 0003 0003 0003 0002 -33 0005 0005 0005 0004 .0004 .0004 0004 0004 0004 0003 -32 0007 -3.1 0010 .0007 0006 0006 .0006 .0006 0006 0005 .0005 0005 0009 .0009…

In a recent awards ceremony, the age of the winner for best actor was 38 and the age of the winner for best actress was 51. For all best actors, the mean age is 48.7 years and the standard deviation is 7.1 years. For all best actresses, the mean age is 34.4 years and the standard deviation is 10.2 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain. Since the z score for the actor is z= and the z score for the actress is z = the V had the more extreme age.