1. The mean systolic blood pressure in a certain population of men between the ages of 20 and 24 is known to be 120 mm Hg, with a standard deviation of 20 mm Hg. a) A 22-year-old man is selected at random. What is the probability that a man selected at random from the specified population will have a systolic blood pressure less than or equal to 150 mm Hg? b) A 20-year-old man selected at random had a systolic blood pressure of 160 mm Hg. How far does this value lie value above the population mean, in units of standard deviation? c) Ninety–five percent of all systolic blood pressure readings for the men comprising this population will lie between which two values? Between which two values will 90% of all systolic blood pressure readings lie?
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!
1. The mean systolic blood pressure in a certain population of men between the ages of 20 and 24 is known to be 120 mm Hg, with a standard deviation of 20 mm Hg.
a) A 22-year-old man is selected at random. What is the probability that a man selected at random from the specified population will have a systolic blood pressure less than or equal to 150 mm Hg?
b) A 20-year-old man selected at random had a systolic blood pressure of 160 mm Hg. How far does this value lie value above the population mean, in units of standard deviation?
c) Ninety–five percent of all systolic blood pressure readings for the men comprising this population will lie between which two values? Between which two values will 90% of all systolic blood pressure readings lie?
d) What proportion of readings fall between 100- and 140-mm Hg?
e) What proportion of readings are less than 60 mm Hg or greater than 180 mm Hg?
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