6.5.2

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?

6.5.4

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998).Blood pressure is normally distributed.

a.)State the random variable.

b.)Suppose a sample of size 15 is taken.State the shape of the distribution of the sample mean.

c.)Suppose a sample of size 15 is taken.State the mean of the sample mean.

d.)Suppose a sample of size 15 is taken.State the standard deviation of the sample mean.

e.)Suppose a sample of size 15 is taken.Find the probability that the sample mean blood pressure is more than 135 mmHg.

f.)Would it be unusual to find a sample mean of 15 people in China of more than 135 mmHg?Why or why not?

g.)If you did find a sample mean for 15 people in China to be more than 135 mmHg, what might you conclude?