As shown in your earlier work, assuming the systolic blood pressure among women college students is normally distributed with mean of 114.6 and standard deviation of 14.1. The following questions are very similar to your last assignment except that this time, it is not the probability of one student selected at random, but the probability of the average from a group of students.
a) If 16 students are randomly selected, find the probability that their average systolic blood pressure is between 105 and 125.
b) If 25 students are randomly selected, find the probability that their average systolic blood pressure is greater than 120.
c) If 4 students are randomly selected, find the probability that their average systolic blood pressure is less than 100.
d) If 9 students are randomly selected, find the probability that their average systolic blood pressure is outside of the interval between 100 and 130?
e) Of all possible random samples of 9 students, 95% of their averages are above what value?
f) Of all possible random samples of 30 students, 90% of their averages are between what two values symmetrically distributed around the mean of 114.6?
g) If a recording of the average blood pressure from a random sample of 25 students had only one reading of 110, do you think it is more likely to be a systolic or a diastolic recording? (Must show computations to backup your claim. Hint: Compare the probability of having a systolic BP <110 with the probability of having a diastolic BP >110. The diastolic BP has a mean of 72.7 and S.D. of 10.1.)
Hypertension is commonly defined as whose with a blood pressure of 140 or above, thus 2.74% of the population of women college students has Hypertension.
h) What is the approximate minimum sample size we need for us to use the normal approximation to study the proportion of hypertension issue in the population?
i) In a random sample of 200 women college students, what is the probability that we see less than 2.5% of them having hypertension?
j) What is the probability that we see between 2% and 3% of them having hypertension in our sample?