Respuesta :
Answer:
The minimum score that an applicant must make on the test to be accepted is 360.
Step-by-step explanation:
Given : A highly selective boarding school will only admit students who place at least 2.5 standard deviations above the mean on a standardized test that has a mean of 300 and a standard deviation of 24.
To find : What is the minimum score that an applicant must make on the test to be accepted?
Solution :
We apply the z formula,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where, z value= 2.5
[tex]\mu=300[/tex] is the mean of the population
[tex]\sigma=24[/tex] is the standard deviation
x is the sample mean.
Substituting the values in the formula,
[tex]2.5=\frac{x-300}{24}[/tex]
[tex]2.5\times24=x-300[/tex]
[tex]60=x-300[/tex]
[tex]x=60+300[/tex]
[tex]x=360[/tex]
Therefore, The minimum score that an applicant must make on the test to be accepted is 360.
The minimum score that an applicant must make on the test to be accepted is 360 and this can be determined by using the z formula.
Given :
A highly selective boarding school will only admit students who place at least 2.5 standard deviations above the mean on a standardized test that has a mean of 300 and a standard deviation of 24.
The formula of z can be used in order to determine the minimum score that an applicant must make on the test to be accepted. The z formula is given by:
[tex]\rm z = \dfrac{x - \mu}{\sigma}[/tex]
Now, substitute the values of the known terms in the above formula.
[tex]2.5=\dfrac{x - 300}{24}[/tex]
Cross multiply in the above equation.
[tex]2.5\times 24 = x - 300[/tex]
60 = x - 300
x = 360
So, the minimum score that an applicant must make on the test to be accepted is 360.
For more information, refer to the link given below:
https://brainly.com/question/21328250
