Respuesta :
Answer:
14.64%
Step-by-step explanation:
P(90<X<100) = normalcdf(90,100,82,8) = 0.1464308262 ≈ 0.1464 ≈ 14.64%
Therefore, about 14.64% of the scores are greater than 90.
By calculating the CDF of normal distribution, the percentage of scores that are greater than 90 are 14.6%.
What is CDF function of normal distribution?
The CDF function of a Normal distribution is calculated by translating the random variable to the Standard Normal, and then looking up a value from the precalculated "Phi" function (Φ), which is the cumulative density function of the standard normal. The Standard Normal, often written Z, is a Normal with mean 0 and variance 1. Thus, Z∼N(μ=0,σ²=1).
Let x1, x2, .... be the scores on the test.
X ~ N (82, 64)
[tex]= P(90 < X < 100) \\\\= P(\frac{90 -82 }{8} < \frac{X - 82}{8} < \frac{100-82}{8} ) \\\\= P(1 < \frac{X - 82}{8} < \frac{18}{8}) \\\\P(1 < Z < \frac{18}{8})\\ \\[/tex]
P(90 < X < 100) = Φ(18/8) - Φ(1) = 0.146 (using norm.s.dist function in excel)
Learn more about CDF function of normal distribution here
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