The lengths of home runs hit by players for the Mets have approximately a normal distribution with μ = 399 feet and a standard deviation of σ=31.16 feet. Suppose that we randomly select 81 home runs hit by players of the Mets. Let X be the random variable representing the mean length of home runs in feet and let Xtot be the random variable representing the sum of the lengths of the home runs in feet for the 81 selected home runs. d) About how many of the 81 sampled home runs have length between 400 and 420 feet? (nearest integer) e) What is the standard deviation of the distribution of X? f) What is the standard deviation of the distribution of Xtot?
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 lengths of home runs hit by players for the Mets have approximately a
d) About how many of the 81 sampled home runs have length between 400 and 420 feet? (nearest integer)
e) What is the standard deviation of the distribution of X?
f) What is the standard deviation of the distribution of Xtot?
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