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SpyIntel [72]
2 years ago
7

Given the mean of a random variable, X, is 10 and P(X < 11) = 0.67. Find the standard deviation.

Mathematics
1 answer:
Taya2010 [7]2 years ago
4 0

Answer:

Step-by-step explanation:

This is the problem we need to solve:

z=\frac{x_i-\bar{x}}{\sigma} and we have everything but the z-score (which we find from a table) with our main unknown being the standard deviation.

If the probability that a random variable that is less than 11 is .67, we first have to find the z-score from the table that is closest to .67, and there are 2:

P(z < .43) = .66640 and P(z < .44) = .67003

We'll use z = .44

.44=\frac{11-10}{\sigma} and

.44=\frac{1}{\sigma} and

\sigma=\frac{1}{.44} so

σ = 2.27 (check it; it works!)

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