Suppose that the foot length of a randomly chosen adult male is a normal random variable with mean μ=11μ=11 and standard deviation σ=1.5σ=1.5. With this information complete the following and fill in blanks. 1) a) What is the probability that a randomly chosen adult male will have a foot length between 8 and 14 inches? P(8 < r < 14) = _____ or ______% b) An adult male is almost guaranteed (0.997 probability) to have a foot length between what two values? P(_____< r < ______)= 0.997 2) The probability is only 2.5 % that an adult male will have a foot length greater than how many inches? P(r > _____) =0.025 3) What is the probability that a randomly selected male will have a foot length between 8 and 12.5 inches? P(8 < r < 12.5) = _______ or ________%
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!
Suppose that the foot length of a randomly chosen adult male is a normal random variable with mean μ=11μ=11 and standard deviation σ=1.5σ=1.5. With this information complete the following and fill in blanks.
1)
a) What is the probability that a randomly chosen adult male will have a foot length between 8 and 14 inches? P(8 < r < 14) = _____ or ______%
b) An adult male is almost guaranteed (0.997 probability) to have a foot length between what two values? P(_____< r < ______)= 0.997
2) The probability is only 2.5 % that an adult male will have a foot length greater than how many inches? P(r > _____) =0.025
3) What is the probability that a randomly selected male will have a foot length between 8 and 12.5 inches? P(8 < r < 12.5) = _______ or ________%
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