answer to 6.4.4

6.3.10 The mean yearly rainfall in Sydney, Australia, is about 137 mm and the standard deviation is about 69 mm ("Annual maximums of," 2013). Assume rainfall is normally distributed. b. ) State the random variable. Find the probability that the yearly rainfall is less than 100 mm. Vc.) Find the probability that the yearly rainfall is more than 240 mm. Ld.) Find the probability that the yearly rainfall is between 140 and 250 mm. e.) If a year has a rainfall less than 100mm, does that mean it is an unusually dry year? Why or why not? f.) What rainfall amount are 90% of all yearly rainfalls more than? 6.4.4 Annual rainfalls for Sydney, Australia are given in table #6.4.6. ("Annual maximums of," 2013). Can you assume rainfall is normally distributed? Mes is S.I motel/I and the Table #6.4.6: Annual Rainfall in Sydney, Australia 146.8 383 90.9 178.1 267.5 95.5 156.5 180 90.9 139.7 200.2 171.7 187.2 184.9 70.1 58 84.1 55.6 133.1 271.8 135.9 71.9 99.4 110.6 47.5 97.8 122.7 58.4 154.4 173.7 118.8 88 84.6 171.5 254.3 185.9 137.2 138.9 96.2 85 45.2 74.7 264.9 113.8 133.4 68.1 156.4 6.5.2 overs being very come A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21. a.) If you take a sample of size 10, can you say what the shape of the distribution for the sample mean is? Why? b.) For a sample of size 10, state the mean of the sample mean and the standard deviation of the sample mean. c.) For a sample of size 10, find the probability that the sample mean is more than 241. d.) If you take a sample of size 35, can you say what the shape of the distribution of the sample mean is? Why? ole mean and the standard deviation of