A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21.

1). If you take a sample of size 10, can you say what the shape of the distribution for the sample mean is? please give reason(s)?

2). For a sample of size 10, state the mean of the sample mean and the standard deviation?

3). For a sample of size 10, find the probability that the sample mean is more than 241.

4). If you take a sample of size 35, can you say what the shape of the distribution of the sample mean is? and give reason(s)?

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

6). Compare your answers in part 3 and 5, why is one smaller than the other?