In a normal distribution, $x = 65$ has $z = 1.5$ and $x = 45$ has $z = -0.5$ . What are the mean and the standard deviation?

\mu = 55,\ \sigma = 10

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\mu = 50,\ \sigma = 20

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\mu = 40,\ \sigma = 10

Correct answerYour answer

\mu = 50,\ \sigma = 10

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$65 = \mu + 1.5\sigma$ and $45 = \mu - 0.5\sigma$ . Subtracting: $20 = 2\sigma$ , so $\sigma = 10$ .
Then $\mu = 45 + 5 = 50$ .

Worth noting

$\mu = 55$ is the midpoint of 45 and 65, but the two values are not equally far from the mean.

Ten questions from Normal Distribution, at your own pace.

In a normal distribution, x=65x = 65x=65 has z=1.5z = 1.5z=1.5 and x=45x = 45x=45 has z=−0.5z = -0.5z=−0.5. What are the mean and the standard deviation?