Question

Instructions: Be sure to define all random variables/events used in probability calculations. You should obtain “exact” probabilities from R rather than giving approximate probabilities using the 68-95-99.7 rule. Provide any code you use (final computed values are not sufficient). I strongly recommend that you create a Jupyter Notebook for this assignment, embedding your written comments in Markdown cells.

2. The systolic blood pressure for female diabetics between the ages of 30 and 34 has mean 131 mmHg and standard deviation = 12 mmHg.

a. Do you have enough information to compute (at least approximately) the proportion of individuals in this population who have blood pressure greater than 150 mmHg? If so, provide this value. If not, explain why.

b. Do you have enough information to compute (at least approximately) the probability that the average blood pressure in a random sample of 80 individuals from this population will be greater than 133 mmHg? If so, provide this value and a justification. If not, explain why.

Answer 1

Solution:-

2)

Mean = 131, S.D = 12

a) The proportion of individuals in this population who have blood pressure greater than 150 is 0.0567.

x = 150

By applying normal distribution:-

z = 1.5833

P(z > 1.5833) = 0.0567

b) The probability that the average blood pressure in a random sample of 80 individuals from this population will be greater than 133 mmHg is 0.068.

x = 133

By applying normal distribution:-

z = 1.491

P(z > 1.491) = 0.068

Yes, we have enough information to compute the probability that the average blood pressure in a random sample of 80 individuals from this population will be greater than 133 mmHg.