Question: 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,

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?

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?

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