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? No, because you would have to refer to the central limit theorem which states that you would need larger data set (greater than 30) to show normal distribution.

b.)For a sample of size 10, state the mean of the sample mean and the standard deviation of the sample mean. Mean of the sample is 245. SD is 21/square root of 10=6.641

c.)For a sample of size 10, find the probability that the sample mean is more than 241. Using the calculator app normalcdf(241,1e99,245,6.641)=0.7265

d.)If you take a sample of size 35, can you say what the shape of the distribution of the sample mean is?Why?

e.)For a sample of size 35, state the mean of the sample mean and the standard deviation of the sample mean.

f.)For a sample of size 35, find the probability that the sample mean is more than 241.

g.)Compare your answers in part c and f.Why is one smaller than the other?