Question

Assume that a normal distribution of data has a mean of 13 and a standard deviation of 3. Use the 68minus 95minus99.7 rule to find the percentage of values that lie below 4 .

Answer 1

Given that,

Data follows a normal distribution with mean of 13 and a standard deviation of 3.

68-95-99.7 rule says that :

• About 68% of values fall within one standard deviation of the mean.
• About 95% of the values fall within two standard deviations from the mean.
• Almost all of the values — about 99.7% — fall within three standard deviations from the mean.

Now we have to find percentage of values that lie below 4 .

That is to find P(X < 4)

Z-score for x = 4 is,

z = (x - mean) / sd

z = (4 - 13) / 3 = -3

NOw we have to find P(Z < -3)

By using excel,

P(Z <-3) = 0.0013 = 0.0013*100 = 0.13%