Question

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.

1. State the random variable.
2. Suppose a sample of size 15 is taken. State the shape of the distribution of the sample mean.
3. Suppose a sample of size 15 is taken. State the mean of the sample mean.
4. Suppose a sample of size 15 is taken. State the standard deviation of the sample mean.
5. Suppose a sample of size 15 is taken. Find the probability that the sample mean blood pressure is more than 135 mmHg.
6. Would it be unusual to find a sample mean of 15 people in China of more than 135 mmHg? Why or why not?
7. If you did find a sample mean for 15 people in China to be more than 135 mmHg, what might you conclude?

6.5.6

The mean cholesterol levels of women age 45-59 in Ghana, Nigeria, and Seychelles is 5.1 mmol/l and the standard deviation is 1.0 mmol/l (Lawes, Hoorn, Law & Rodgers, 2004). Assume that cholesterol levels are normally distributed.

1. State the random variable.
2. Find the probability that a woman age 45-59 in Ghana has a cholesterol level above 6.2 mmol/l (considered a high level).
3. Suppose doctors decide to test the woman’s cholesterol level again and average the two values. Find the probability that this woman’s mean cholesterol level for the two tests is above 6.2 mmol/l.
4. Suppose doctors being very conservative decide to test the woman’s cholesterol level a third time and average the three values. Find the probability that this woman’s mean cholesterol level for the three tests is above 6.2 mmol/l.
5. If the sample mean cholesterol level for this woman after three tests is above 6.2 mmol/l, what could you conclude?

Answer 1

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.

State the random variable.

Answer)

Random.variable is blood pressure of people in China

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

Shape is normal

As according to the central limit theorem samples taken from.the normally distributed population are normally distributed

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

Mean is same as population mean = 128

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

Standard deviation = s.d/√n = 23/√15 = 5.93857446418

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

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

P(x>135)

Z = (x-mean)/s.d

Z = (135-128)/(23/√15) = 1.18

From z table, P(z>1.18) = 0.1190

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

No as the probability is large enough

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

Answer)

It is not unusual to find sample mean more than 135 as probability is greater than 5%