Respuesta :
Answer:
68% of jazz CDs play between 45 and 59 minutes.
Step-by-step explanation:
The correct question is: The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).
According to the 68-95-99.7 rule, what percentage of jazz CDs play between 45 and 59 minutes?
Let X = playing time of jazz CDs
SO, X ~ Normal([tex]\mu=52, \sigma^{2} =7[/tex])
The z-score probability distribution for the normal distribution is given by;
                  Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)
Now, according to the 68-95-99.7 rule, it is stated that;
- 68% of the data values lie within one standard deviation points from the mean.
- 95% of the data values lie within two standard deviation points from the mean.
- 99.7% of the data values lie within three standard deviation points from the mean.
Here, we have to find the percentage of jazz CDs play between 45 and 59 minutes;
  For 45 minutes, z-score is =  [tex]\frac{45-52}{7}[/tex]  = -1
  For 59 minutes, z-score is =  [tex]\frac{59-52}{7}[/tex]  = 1
This means that our data values lie within 1 standard deviation points, so it is stated that 68% of jazz CDs play between 45 and 59 minutes.
