Question

The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).

Answer 1

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($\mu=52, \sigma^{2} =7$)

The z-score probability distribution for the normal distribution is given by;

                                    Z  =  $\frac{X-\mu}{\sigma}$  ~ 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 =  $\frac{45-52}{7}$  = -1

   For 59 minutes, z-score is =  $\frac{59-52}{7}$  = 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.