The earth's seasons are caused by a 23.4-degree tilt of the Earth's axis to the orbital plane, and this tilt is also responsible for the variance in the number of hours of daylight. In boston there are 12 hours of daylight at the vernal equinox in Septemer. There are about 15 hours of daylight at the summer solstice in June and about 9 hours of daylight at the winter solstice in December. Part 1: Making the horizontal axis as time in months and the vertical axis as hours of daylight and beginning at the vernal equinox in March, make a graph of hours of daylight versus time over two years. Part 2: Identify the amplitude, median level, and period of the graph you made in part 1. Part 3: make a sine wave that models hours of daylight. Part 4: How many additional hours of daylight are there in August after the vernal equinox?
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 earth's seasons are caused by a 23.4-degree tilt of the Earth's axis to the orbital plane, and this tilt is also responsible for the variance in the number of hours of daylight. In boston there are 12 hours of daylight at the vernal equinox in Septemer. There are about 15 hours of daylight at the summer solstice in June and about 9 hours of daylight at the winter solstice in December.
Part 1: Making the horizontal axis as time in months and the vertical axis as hours of daylight and beginning at the vernal equinox in March, make a graph of hours of daylight versus time over two years.
Part 2: Identify the amplitude, median level, and period of the graph you made in part 1.
Part 3: make a sine wave that models hours of daylight.
Part 4: How many additional hours of daylight are there in August after the vernal equinox?
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