Coursepack, p. 6 MAT 133: 8.1 WS 3, p.2 MIOG 3. A study found that systolic blood pressure was normally distributed with a mean of 106 SD 8 millimeters of mercury (mmHg) and a standard deviation of 8 mmHg. The systolic blood pressure levels of 42 random patients in the Detroit Area are found. a) Verify that the three conditions for the Central Limit Theorem for means are met. Give explanations, and be specific. b) Describe the sampling distribution (shape, center, spread) of the mean systolic blood pressure for the random sample. (Using symbols and formulas as necessary. Give 4 decimal places for spread.) c) Find the probability that the mean for the random sample is less than 107. (Give 4 decimal places and P(X) notation from StatCrunch, circling the answer) P ( x 2 10 4 ) = 0.54973822 0 . 5494 d) Find the 20th percentile of the sample means. (Give units) P (x = 49, 26 40 ) =. 20 e) Suppose that the 42 random patients have a mean systolic blood pressure level above 112, which is unusual with a probability of 0.0006. Give three different explanations for this result. very 1 , some people have high Blood pressure 2. The study could have been on people that are for example athletes as good BP or everyone is healthys Sample bias 3 . Data entry error