The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean ? = 120 and standard deviation ? = 18. (a) Calculate the z-scores for the male systolic blood pressures 100 and 140 millimeters. (Round your answers to two decimal places.) 100 mm z = 140 mm z = (b) If a male friend of yours said he thought his systolic blood pressure was 2.5 standard deviations below the mean, but that he believed his blood pressure was between 100 and 140 millimeters, what would you say to him? (Enter your numerical answer to the nearest whole number.) He is ---Select--- (correct or incorrect) because 2.5 standard deviations below the mean would give him a blood pressure reading of millimeters, which is ---Select--- (below, above or in) the range of 100 to 140 millimeters.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The systolic blood pressure (given in millimeters) of males has an approximately
? = 120
and standard deviation
? = 18.
(a) Calculate the z-scores for the male systolic blood pressures 100 and 140 millimeters. (Round your answers to two decimal places.)
| 100 mm | z | = | |
| 140 mm | z | = |
(b) If a male friend of yours said he thought his systolic blood pressure was 2.5 standard deviations below the mean, but that he believed his blood pressure was between 100 and 140 millimeters, what would you say to him? (Enter your numerical answer to the nearest whole number.)
He is ---Select--- (correct or incorrect) because 2.5 standard deviations below the mean would give him a blood pressure reading of millimeters, which is ---Select--- (below, above or in) the
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