College

Assume that a normal distribution of data has a mean of 21 and a standard deviation of 2. Use the 68-95-99.7 rule to find the percentage of values that lie above 25.

Answer :

Approximately 2.5% of the values lie above 25.

We first calculate how many standard deviations above the mean 25 is:

Number of standard deviations[tex]= \(\frac{25 - 21}{2} = 2\)[/tex]

Since 25 is 2 standard deviations above the mean, we can use the 68-95-99.7 rule:

  • Approximately 95% of the data falls within two standard deviations above and below the mean.
  • Therefore, approximately [tex]\(\frac{100 - 95}{2} = 2.5\%\)[/tex] of the data falls above two standard deviations above the mean.

So, approximately 2.5% of the values lie above 25.