Construct a 95% Z-interval or a 95% t-interval about the population mean. Assume the data come from a population that is approximately normal v Fifteen randomly selected men were asked to run on a treadmill for 6 minutes. After the 6 minutes, their pulses were measured and the following data were o 105 94 98 88 104 101 99 85 84 124 122 114 97 101 90 O (93.7, 107.1); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 93.7 and 107.1 beats per minute. O (94.9, 105.9); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 94.9 and 105.9 beats per minute. O (95.2, 105.6); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 95.2 and 105.6 beats per minute. O (94.2, 106.6); we are 959% confident that the mean pulse rate of men after 6 minutes of exercise is between 94.2 and 106.6 beats per minute.
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!
x | (x-xbar)^2 |
105 | 21.16 |
94 | 40.96 |
98 | 5.76 |
88 | 153.76 |
104 | 12.96 |
101 | 0.36 |
99 | 1.96 |
85 | 237.16 |
84 | 268.96 |
124 | 556.96 |
122 | 466.56 |
114 | 184.96 |
97 | 11.56 |
101 | 0.36 |
90 | 108.16 |
The mean is given by
The standard deviation is given by
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