Out of 2000 random but normally distributed numbers with a mean of 45 and a standard deviation of x, approximately 1360 numbers are found to be between 40 and 50. What is the value of x?

Question

Efrain

Mathematics

9 April, 16:04

Out of 2000 random but normally distributed numbers with a mean of 45 and a standard deviation of x, approximately 1360 numbers are found to be between 40 and 50. What is the value of x?

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Answers (1)

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Brenton Campbell · Answer 1

First we have to find which percent of 2000 numbers are 1360 numbers.

p = 1360 / 2000 * 100 = 68 %

It means that for normal distribution the values 40 and 50 are within + / - 1 standard deviation from the mean (45).

45 - x = 40 and 45 + x = 50.

x = 45 - 40 = 50 - 45 = 5

Answer:

x = 5