Question 14:

Asked on October 23, 2007

Tags: Z-Score , Normal Curve , Standard Deviation , Normally Distributed

1

Answer:

No answer provided yet.

The amount of Jen's monthly bill is normally distributed with a mean of $66 and a standard deviation of $8. What percentage of her phone bills are between $42 and $90? To answer this, think of the properties of the normal curve, 68% of the values fall within one standard deviation, 95% of the values fall within 2 standard deviations and 99% of the values fall within 3 standard deviations. Remember, this is 3 standard deviations above and below the mean.

In the example above, how many standard deviations are there above and below the mean? Above the mean there is 90-66 = $24. Below the mean there are is 66-42 = $24. Both values are symmetrical, which a normal distribution by definition is. Since the standard deviation is 8, you can see that 3 standard deviations above and below the mean (24/8=3). So just knowing the properties of the normal curve we know that about 99% of Jen