Vincenzo De Cerce was diagnosed with high blood pressure. He was able to keep hi
ID: 3173097 • Letter: V
Question
Vincenzo De Cerce was diagnosed with high blood pressure. He was able to keep his blood pressure in control for several months by taking blood pressure medicine (amlodipine besylate). De Cerces blood pressure is monitored by taking three readings a day, in early morning, at midday, and in the evening. (a) During this period, the probability distribution of his systolic blood pressure reading had a mean of 130 and a standard deviation of 6. If the successive observations behave like a random sample from this distribution, find the mean and standard error of the sampling distribution of the sample mean for the three observations each day. Use 3 decimal places. Mean = Standard error = (b) Suppose that the probability distribution of his blood pressure readings is normal. What is the shape of the sampling distribution of the sample mean? Non-normal, because the sample size is too small. Normal, because the population is normally distributed. (c) Refer to (b). What is the probability that the sample mean exceeds 140, which is considered problematically high? Use 3 decimal places.
Explanation / Answer
Result:
Vincenzo De Cerce was diagnosed with high blood pressure. He was able to keep his blood pressure in control for several months by taking blood pressure medicine (amlodipine besylate). De Cerces blood pressure is monitored by taking three readings a day, in early morning, at midday, and in the evening.
Mean = 130
Standard error = 6/sqrt(3) =3.464
Normal, because the population is normally distributed.
(c) Refer to (b). What is the probability that the sample mean exceeds 140, which is considered problematically high? Use 3 decimal places.
Z value for 140, z =(140-130)/3.464 =2.89
P( mean x >140) = P( z >2.89)
=0.0019
=0.002 ( 3 decimals).
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