An athletics coordinator collected the 100-meter sprint times for 15-year old students at Ryde Secondary College. The sprint time assumes to follow a normal distribution with a mean of = 14.25 seconds and a variance of 22= 0.5184 seconds22.

Draw diagrams to help you solve the following problems

(1 mark) For a group of 42 fifteen-year students randomly selected at Ryde Secondary College, how many of them will have a 100-meter sprint time of 14.17 seconds or less? Answer (integer)

(2 mark) How fast does a 15-year old student at Ryde Secondary College have to run to be the fastest 22%% of 100-meter sprinters? Answer (3dp) (Hint: Draw a diagram to help check whether your answer makes sense or not)

(2 mark) The sprint time for a randomly selected 15-year student at Ryde Secondary College ranges between 1.147 standard deviations below the mean of a standard normal distribution and 1.235 standard deviations above the mean of a standard normal distribution. What is the probability of another randomly selected 15-year student having the same sprint time range? Answer (3dp) (Hint: Draw a standard normal diagram and clearly label the information onto the graph. Be careful with the sign.)