The Grand Canyon Skywalk is a viewing platform located 3,000 ft over the river in the base of Canyon. According to Wikipedia, the platform is rated for a maximum of 120 people at one time. Data from a statistics book on the weights of adults is given below. Assume male and female adult weights are normally distributed. Males Females Mean 182.9 lb 165.0 lb Std. Dev. 40.8 lb 45.6 lb Find the probability that 1 randomly selected adult male has a weight greater than 200 lbs.
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!
Let X denote the male adult weights and it follows normal distribution with mean of and standard deviation of
The probability that 1 randomly selected adult male has a weight greater than 200 lbs is,
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