Answer :
Approximately 34% of the values lie below 23.
Given that the mean [tex](\(\mu\))[/tex] is 19 and the standard deviation[tex](\(\sigma\))[/tex]is 4, we can calculate the value of one standard deviation:
One standard deviation [tex](\(\sigma\))[/tex] = 4
To find the percentage of values that lie below 23, we need to find how many standard deviations away 23 is from the mean and then use the 68-95-99.7 rule.
[tex]\[ \text{Number of standard deviations} = \frac{\text{value} - \mu}{\sigma} = \frac{23 - 19}{4} = \frac{4}{4} = 1 \][/tex]
Since 23 is 1 standard deviation above the mean, we can use the 68-95-99.7 rule to find the percentage of values that lie below 23:
- Approximately 68% of the data falls within one standard deviation below and above the mean.
- Therefore, approximately [tex]\( \frac{68}{2} = 34\% \)[/tex] of the data falls below one standard deviation above the mean.
So, approximately 34% of the values lie below 23.
