Tall clubs: The social organization Tall Clubs International has a requirement that women must be at least 70 in tall. Assume that women have normally distributed heights with a mean of 63.7 in and a standard deviation of 2.9 in. a. Find the percentage of women who satisfy the height requirement. BMI 15.9 18.7 24.2 28.7 28.2 28.9 28.9 28.9 29.0 29.1 29.3 31.4 59.0 b.If the height requirement is to be changed so that the tallest 2.5% of women are eligible, what is the new height requirement?
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!
- Tall clubs: The social organization Tall Clubs International has a requirement that women must be at least 70 in tall. Assume that women have
normally distributed heights with amean of 63.7 in and a standard deviation of 2.9 in.
a. Find the percentage of women who satisfy the height requirement.
|
BMI |
|
15.9 |
|
18.7 |
|
24.2 |
|
28.7 |
|
28.2 |
|
28.9 |
|
28.9 |
|
28.9 |
|
29.0 |
|
29.1 |
|
29.3 |
|
31.4 |
|
59.0 |
b.If the height requirement is to be changed so that the tallest 2.5% of women are eligible, what is the new height requirement?
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