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SYSTOLIC BLOOD PRESSURE Chapter 7 – Section 7.2 – Distribution of Sample Means 2) For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 mm Hg and a standard deviation of 13.1 mm Hg. a) Give the shape, mean and standard deviation of the distribution of sample means for samples of size 36. Notice: the population is 18-24 year old women and the variable X is their systolic blood pressure (in mm Hg) X is Normal with 114.8 and 13.1 According to the Central Limit Theorem, the distribution of sample means is normal for any sample size because X is normally distributed. Hence, for samples of size 36, the distribution of x-bar is also normal with x 114.8 x n 13.1 2.18 36 b) What is the probability that a sample of 36 women of this age group has a mean systolic blood pressure of at least 121 mm Hg? 121 114.8 ) P( z 2.84) 1 .9977 .0023 13.1 36 13.1 2 With calculator: normalcdf(121, 109 , 114.8, ) = 0.0023~0.002= 1000 36 P( x 121) P( z A mean of 121 would be more likely in a population with mean higher than 114.8, that is why we conclude....see **** c) If the population mean is 114.8, the probability of obtaining a sample of size 36 with a mean of 121 or more is __0.002_____. So, for samples of size 36, about __2__ samples in 1000 will have a sample mean of 121 or more when the population mean is 114.8. Because this event only happens _2__ out of __1000____ times, we consider it to be usual/unusual. d) What may this result suggest? If the population mean is 114.8, it’s very unusual to observe a sample of size 36 with a mean of 121 or more. ***********This unusually high result may suggest that “probably” the sample was selected from a population with mean higher than 114.8. 1