Question

- Blood Pressure For women aged 18–24, systolic blood pressures (in mm Hg) are nor- mally distributed with a mean of 114.8 and a standard deviation of 13.1 (based on data from the National Health Survey). Hypertension is commonly defined as a sys- tolic blood pressure above 140. a. If a woman between the ages of 18 and 24 is randomly selected, find the probabil- ity that her systolic blood pressure is greater than 140. b. If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140. c. Given that part(b) involves a sample size that is not larger than 30, why can the central limit theorem be used? d. If a physician is given a report stating that 4 women have a mean systolic blood pressure below 140, can she conclude that none of the women have hypertension (with a blood pressure greater than 140)?

Answer 1

ANSWER a) Normal distribution with M=114.8,==18. x=140 = RM 140 1148 13-1 1992 -2 P(x >140) P(Z >1.92) = 1-P (Z <1.92) b) M = 1148 =1-0.9726 0.0274 Jn = 13-1 TE = 6:55 x=140 140 - 114.8 6.55 = 3.85 P(x>140) =P (2>3.85) -1-p(2<3.35) = -0.9999 e) since the \ ܩܩܩ. ܘ Osiginal distribution is normal the central can be used in part (6) Even through limit theorem the sample size does not Exceed 30 d) The mean (an be less than 140 when one or more of the values is greater than 140 CS Scanned with CamScanner