Answer:
The percentage of people should be seen by the doctor between 13 and
17 minutes is 68% ⇒ 2nd term
Step-by-step explanation:
* Lets explain how to solve the problem
- Wait times at a doctor's office are typically 15 minutes, with a standard
deviation of 2 minutes
- We want to find the percentage of people should be seen by the
doctor between 13 and 17 minutes
* To find the percentage we will find z-score
∵ The rule the z-score is z = (x - μ)/σ , where
# x is the score
# μ is the mean
# σ is the standard deviation
∵ The mean is 15 minutes and standard deviation is 2 minutes
∴ μ = 15 , σ = 2
∵ The people should be seen by the doctor between 13 and
17 minutes
∵ x = 13 and 17
∴ z = [tex]\frac{13-15}{2}=\frac{-2}{2}=-1[/tex]
∴ z = [tex]\frac{17-15}{2}=\frac{2}{2}=1[/tex]
- Lets use the standard normal distribution table
∵ P(z > -1) = 0.15866
∵ P(z < 1) = 0.84134
∴ P(-1 < z < 1) = 0.84134 - 0.15866 = 0.68268 ≅ 0.68
∵ P(13 < x < 17) = P(-1 < z < 1)
∴ P(13 < x < 17) = 0.68 × 100% = 68%
* The percentage of people should be seen by the doctor between
13 and 17 minutes is 68%
Disclaimer: i accidentally rated my own answer with one star; i assure you this is completely trustworthy.
Here's a simpler version of what the guy above me did.
your answer is 68%.
Now, why is that?
Let's start by identifying the mean and the standard deviation of the equation.
Mean- 15
Standard deviation- 2
Don't forget the "rule of three" for standard deviation.
68% of the results would be within one standard deviation from the mean
95% would be within two deviations
99.7 would be between three deviations from the mean.
the standard deviation in this equation is two, so let's subtract the smaller of the other two numbers given to us in the equation from the mean to see how many deviations away from the mean it is.
15 - 1 = 2
ONE DEVIATION AWAY
Now let's do the reverse with the other number, which is larger than the mean.
17 - 15 = 2
ONE DEVIATION AWAY.
THE RULE OF THREE STATES THAT 68 PERCENT OF ALL RESULTS WILL BE WITHIN ONE STANDARD DEVIATION OF THE MEAN, JUST AS THE GIVEN NUMBERS ARE.
Therefore, your answer is 68%
make this brainliest so people have a simpler way to solve problems like these from now on.
