Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with μ=111μ=111 and σ=15σ=15. (a) What proportion of children aged 13 to 15 years old have scores on this test above 93 ? (NOTE: Please enter your answer in decimal form. For example, 45.23% should be entered as 0.4523.) (b) Enter the score which marks the lowest 30 percent of the distribution. (c) Enter the score which marks the highest 10 percent of the distribution.
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!
Scores on a certain intelligence test for children between ages 13 and 15 years are approximately
(a) What proportion of children aged 13 to 15 years old have scores on this test above 93 ? (NOTE: Please enter your answer in decimal form. For example, 45.23% should be entered as 0.4523.)
(b) Enter the score which marks the lowest 30 percent of the distribution.
(c) Enter the score which marks the highest 10 percent of the distribution.
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