he full height of a certain species of tree has a normal probability distribution with a mean of 195.6 ft and a standard deviation of 7.5 ft. State the random variable. ¯x = the height of a certain species of tree ¯x = the mean height of a certain species of tree x = the height of a certain species of tree x = the diameter of a certain species of tree A tree of this type grows in my backyard, and it stands 187.4 feet tall. Find the probability that the height of a randomly selected tree is shorter than mine. Round to three decimal places. Which is the notation for the probability that the height is shorter than mine? P(x < 187.4) P(¯x < 195.6) P(¯x > 195.6) P(x > 195.6) P(¯x< 187.4) P(x < 195.6)
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 full height of a certain species of tree has a
- ¯x = the height of a certain species of tree
- ¯x = the mean height of a certain species of tree
- x = the height of a certain species of tree
- x = the diameter of a certain species of tree
A tree of this type grows in my backyard, and it stands 187.4 feet tall. Find the probability that the height of a randomly selected tree is shorter than mine. Round to three decimal places.
Which is the notation for the probability that the height is shorter than mine?
- P(x < 187.4)
- P(¯x < 195.6)
- P(¯x > 195.6)
- P(x > 195.6)
- P(¯x< 187.4)
- P(x < 195.6)
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