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An athletics coordinator collected the 100-meter sprint times for 15-year old students at Riverside Girls High School. The sprint time assumes to follow a normal distribution with a mean of p: 14.61 seconds and a variance of 02: 0.7744 seconds2. Draw diagrams to help you solve the following problems 1. (1 mark) For a group of 48 fifteen-year students randomly selected at Riverside Girls High School, how many of them will have a 100meter sprint time of 15.44 seconds or less? (integer) 2. (2 mark) How fast does a 15-year old student at Riverside Girls High School have to run to be the fastest 23% of 100-meter sprinters? (3dp) (Hint: Draw a diagram to help check whether your answer makes sense or not) 3. (2 mark) The sprint time for a randomly selected 15-year student at Riverside Girls High School ranges between 1.942 standard deviations below the mean of a standard normal distribution and 0.107 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? (3dp) (Hint: Draw a standard normal diagram and clearly label the information onto the graph. Be careful with the sign.)

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