Respuesta :
We can use the empirical rule (also called 68-95-99.7 rule) to evaluate the percentage of people.
99.7% of people should be sen by the doctor between 11 and 23 minutes for this to be considered a normal distribution.
Thus, Option D: 99.7% is correct.
Given that:
- The typical time interval of wait time is 17 minutes.
- The standard deviation for wait time is 2 minutes.
To find:
Percentage of people that are to be seen by the Doctor for the distribution of wait time to be considered normal distribution.
What is empirical rule for normal distribution?
If [tex]X \sim N(\mu, \sigma)[/tex] (that means, X pertains normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex]), then we have:
[tex]P(\mu - \sigma < X <\mu + \sigma) \approx 68\% = 0.68\\\\P(\mu - 2\sigma < X <\mu + 2\sigma) \approx 95\% = 0.95\\\\P(\mu - 3\sigma < X <\mu + 3\sigma) \approx 99.7\% = 0.997[/tex]
Let X be the random variable tracking the wait time (in minutes) by patients for checkup.
Then we have by given data:
[tex]\mu = 17 \: \rm minutes[/tex]
[tex]\sigma = 2 \: \rm minutes[/tex]
Thus,
[tex]X \sim N(17, 2)[/tex]
The given limits are 11 and 23 minutes or
[tex]11 < X < 23 = 17 - 6 < X < 17 + 6 = \mu - 3\sigma < X < \mu + 3\sigma[/tex]
Thus, the percentage can be calculated by empirical rule as follows:
[tex]P(11 < X < 23 ) = P(\mu - 3\sigma < X < \mu + 3\sigma) = 0.997 = 99.7\%[/tex]
where [tex]\mu = 17, \sigma = 2[/tex].
Thus, 99.7% of people should be sen by the doctor between 11 and 23 minutes for this to be considered a normal distribution.
Thus, Option D: 99.7% is correct.
Learn more about empirical rule here:
https://brainly.com/question/16645539
