Question

The answers are in red. I completely forgot how to approach this type of question. Please go into detail!

One season, the average little league baseball game averaged 2 hours and 54 minutes (174 minutes) to complete. Assume the length of games follows the normal distribution with a standard deviation of 13 minutes. Complete parts a through d below. a. What is the probability that a randomly selected game will be completed in less than 190 minutes? The probability that a randomly selected game will be completed in less than 190 minutes is 0.8908 (Round to four decimal places as needed.) b. What is the probability that a randomly selected game will be completed in more than 190 minutes? The probability that a randomly selected game will be completed in more than 190 minutes is 0.1092 (Round to four decimal places as needed.) c. What is the probability that a randomly selected game will be completed in exactly 190 minutes? The probability that a randomly selected game will be completed in exactly 190 minutes is 0.0000 (Round to four decimal places as needed.) d. What is the completion time in which 97.5% of the games will be finished? About 97.5% of the games will be finished in 199.48 minutes or less. (Round to two decimal places as needed.)

Answer 1

solution:- le = 174 o= 13 7 =X-l 1xc190) = P(Z 190-179, =*44 190 e 190-174 13 =P(2c 1.23) - 0.8907 { from t-table? 0.8907 b) P(xJ190) = 2 I-Plxc 190) 1 - 0.8907 0.1093 c) P(x=190) = P(2=1.23) continuous sx is a random variable Area under curve will be o a L. score for gg.7 percentile = 278 1.96 7 = t- 21.45 = X - 174 1.96 13 » x= [199.48)