You may need to use R studio to do some of the question. Thank you.

Running Times A sports coach is interested in the time it takes Under 15 (U15) boys to run 100 metres. Question 1 Based on the coach's records, the time for U15 boys to run 100 metres can be assumed to follow a normal distribution with a mean of 13.1 seconds and a standard deviation of 0.66 seconds. The probability that a randomly selected boy took more than 12.9 seconds to run 100 metres is 0 0.1905 0.3809 0.6191 000 0.7422 Question 2 Assuming the distribution in Question 1, the probability that a randomly selected boy took more than 12.5 seconds but less than 12.9 seconds to run 100 metres is 0 0.1817 0.1993 0.4225 000 0.8183 Question 3 Assuming the distribution in Question 1, the longest time to run 100 metres that would be in the lowest 5% of the running times is O 11.81 seconds 12.01 seconds 14.19 seconds 000 14.39 seconds Question 4 Suppose that a random sample of 4 boys was selected. Assuming the distribution in Question 1, the probability that the average time to run 100 metres for the 4 boys is less than 12.6 seconds is 0 0.0649 0 0.2244 0 0.5001 0 0.9351 Question 5 Based on the distribution in Question 1, it can be shown that 44.0% of boys have 100 metre times less than 13 seconds. Suppose the coach takes a random sample of 4 boys from his pool. The expected number of boys that have a time less than 13 seconds is O 0.44 o 1.11 o 1.76 O 200 Question 6 Based on the distribution in Question 1, it can be shown that 44.0% of boys have 100 metre times less than 13 seconds. Suppose the coach takes a random sample of 4 boys from his pool. The probability that at least 2 boys have a time less than 13 seconds is 0 0.3643 0 0.4074 0 0.5006 0 0.5926 Question 7 The sports coach claims that the mean time to run 100 metres for U15 girls is longer than that of boys. Suppose / is the mean time to run 100 metres for U15 girls. To test this claim the sports coach should test O Ho : M = 13.1 vs H1 : M > 13.1 O Ho : M = OVs H1 : M