Question

30) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph? A) at most 2.5% C) approximately 16% B) at most 34% D) at most 13.5%

can you tell me how to find each number on the chart?

Answer 1

0 The sto 100 miles per hous e statistician reported that mean serve speed was les per hour (mph and standard deviation of e ses ve speeds was 15 mph. Assume that the statistician also gave us the Information that the distribution of serve speeds cas mound-shaped and symmet HC le normally distribution & XNN(100 (15)) consider, P(745<x<145), 4 = 100,0:15 =5,2 EX- 115 - 100. - o 15 = 1 L N N0o,1) net x = 185, 2 x X=145,2 = x - l = 145-100 3 LUNCO,1) ..P ( 115444145) - P (K 2<3) But placX<b) = P(xcb- P(x<a and p(x< 9) = 1- Dex.>a) P(x < b) = 1-P(x > b). Using this we can write, P(115CX (145)=P(IK2L3) = P(2<3) - P(ZL1) = 1-P (273) - (1 - P1271] - P (271) - P (273) By using standard normal probability table, P(271) = 0.1537 and P (273) = 0.0013 p(115<x<165) = 0.1537 -0.0013 -0,15 24 : percentage of the player's seaves were between 115 and 145 mph is 0.1524X10 0 = 15.24% Tie approximately 16%