Question

Example 1: Among females in the US in a given age cohort, a diastolic blood pressure is normally distributed with mean µ = 95 mm Hg and standard deviation σ = 15 mm Hg. a) What is the probability that a randomly selected woman has a diastolic blood pressure less than 90 mm Hg? b) What is the probability that she has a diastolic blood pressure greater than 95 mm Hg? c) What is the probability that she has a diastolic blood pressure between 65 and 85 mm Hg? d) We selected a large number of random samples of size 20 from smoking females of the same cohort, and we received sampling mean equal to 92.5mm Hg. Can we not reject the hypothesis at the significance level α = 0.05 that this smoking women subgroup has the same mean as population, i.e. H0 : µ = 85.8 mm Hg against HA : µ 6= 85.8?

Example 2: Let p = 0.1 be the probability that a man in a certain age group dies in the next four years. Say we observe 30 such men and we assume independence. Consider the probability P4 that fewer than five of them die in the next four years. Which is the correct answer? A) P4 = 0.5. Explain. B) P4 > 0.5. Explain. C) P4 < 0.5. Explain.

Example 3: Among adults in the US, the distribution of albumin levels in cerebrospinal fluid is roughly symmetric with mean µ = 50mg/100ml and standard deviation σ = 12.7mg/100ml. Suppose that you select repeated samples of size 20 from this population and calculate the mean for each sample. If you were to select a large number of random samples of size 20, the sample variance of the means will be a) larger than population variance b) approximately the same as population variance c) lower than population variance

Example 4: (30 points) 2 At a hospital’s emergency room, patients are classified and 20% of them are critical, 40% are serious, and 40% are stable. Of the critical ones, 31% die; of the serious 15% die, and of stable 0.01% die. Given that a patient dies, then a) the conditional probability that a patient was classified as critical equals to 0.4 b) the conditional probability that a patient was classified as critical is less than 0.4 c) the conditional probability that a patient was classified as critical is greater than 0.4

Example 5: We have data of Serum-cholesterol (measured in mg/100ml): 124.82, 99.2, 124.2, 89.6, 94.19, 95.3, 80.6, 100.3. Which of the following statements is correct? a) the median is larger than mean b) the median is lower than mean c) the median and mean are the same

Example 6: In Denver, Colorado, the distribution of daily measures of ambient nitric acid is skewed to the right, it has mean µ = 1.81micro g/m3 and the standard deviation σ = 2.25micro g/m3 . Then the distribution of means of samples of size 30 selected from this population is a) skewed to the right more than the original sample b) skewed to the right less than the original sample

Answer 1