For an applicant to qualify for a scholarship grant in a certain university, the applicant must belong to the top 5% in an entrance test. If the test has a mean of 100 and a standard deviation of 10, find the lowest possible score to qualify for the scholarship. Assume that the scores are distributed normally. Find the x value that represents the upper 5% of the normal distribution b. Find the area under the normal distribution from 100 to x а. с. Find the corresponding z-value of the area in letter b d. Substitute into the z-score formula, then solve for the value of x
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!
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