jen1598
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I need some help on two questions, which are basically asking me to do the same thing, but there are some different numbers involved in each. Here they are:

A set of data with 1,200 numbers is normally distributed with a mean of 27 and a standard deviation of 4. How many numbers in the data would you expect to be between 23 and 31?

A set of data with 1,200 numbers is normally distributed with a mean of 27 and a standard deviation of 4. How many numbers in the data would you expect to be between 19 and 35?

Thanks for your help in advance. :)

Respuesta :

MathPhys

Answer:

816

1140

Step-by-step explanation:

(1)

Start by finding the z score of each value.

z = (x − μ) / σ

z₁ = (23 − 27) / 4

z₁ = -1

z₂ = (31 − 27) / 4

z₂ = 1

So we're looking at the numbers between -1 and +1 standard deviations.  According to the empirical rule, 68% of a normal curve is in this range.  So 68% of 1200 is:

0.68 × 1200 = 816

(2)

Again, we find the z scores:

z₁ = (19 − 27) / 4

z₁ = -2

z₂ = (35 − 27) / 4

z₂ = 2

This time, we're looking at the numbers between -2 and +2 standard deviations.  According to the empirical rule, 95% of a normal curve is in this range.  So 95% of 1200 is:

0.95 × 1200 = 1140

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