Language. Neurological research has shown that inabout 80% of people language abilities reside in the brain’s left side. Another 10% display right-brain lan-guage centers, and the remaining 10% have two-sided language control. (The latter two groups are mainlyleft-handers.) (Science News, 161, no. 24 [2002])a) We select 60 people at random. Is it reasonable to use a Normal model to describe the possible distribu-tion of the proportion of the group that has left-brain language control? Explain.b) What’s the probability that our group has at least 75%left-brainers?c) If the group had consisted of 100 people, wouldthat probability be higher, lower, or about the same?Explain why, without actually calculating theprobability.d) How large a group would almost certainly guaranteeat least 75% left-brainers? Explain.
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!
about 80% of people language abilities reside in the
guage centers, and the remaining 10% have two-sided
left-handers.) (Science News, 161, no. 24 [2002])
a) We select 60 people at random. Is it reasonable to
tion of the proportion of the group that has left-brain
b) What’s the probability that our group has at least 75%
left-brainers?
c) If the group had consisted of 100 people, would
that probability be higher, lower, or about the same?
Explain why, without actually calculating the
probability.
d) How large a group would almost certainly guarantee
at least 75% left-brainers? Explain.
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