In a normal distribution, $x = 70$ has $z = 2$ and $x = 40$ has $z = -1$ . What are the mean and the standard deviation?

Mean 50, standard deviation 10Correct answerYour answerMean 55, standard deviation 15Correct answerYour answerMean 50, standard deviation 15Correct answerYour answerMean 60, standard deviation 10Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$70 = \mu + 2\sigma$ and $40 = \mu - \sigma$ .
Subtracting: $30 = 3\sigma$ , so $\sigma = 10$ and $\mu = 50$ .

Worth noting

Mean 55 is the midpoint of 40 and 70, which would need the two $z$ -values to be opposites.

Concept: The mean and standard deviation from two values
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsThe standard normal variate

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Ten questions from Normal Distribution, at your own pace.

In a normal distribution, x=70x = 70x=70 has z=2z = 2z=2 and x=40x = 40x=40 has z=−1z = -1z=−1. What are the mean and the standard deviation?

Explanation

In a normal distribution, $x = 70$ has $z = 2$ and $x = 40$ has $z = -1$ . What are the mean and the standard deviation?