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.

a.)Find the probability that the yearly rainfall is less than 100 mm.

b.)Find the probability that the yearly rainfall is more than 240 mm.

c. )Find the probability that the yearly rainfall is between 140 and 250 mm

d.)What rainfall amount are 90% of all yearly rainfalls more than?

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.