Respuesta :
Answer:
79 marks are required to get a B or higher.
Step-by-step explanation:
We have been given that the marks on a statistics test are normally distributed with a mean of 62 and a variance of 225. The instructor wishes to assign Bs or higher to the top 25% of the students in the class.
We will use normal distribution table and z-score formula to solve our given problem.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
z= Z-score,
x = Sample score,
[tex]\mu=\text{Mean}\\\sigma=\text{Standard deviation}[/tex]
We know that standard deviation is equal to square-root of variance, so SD for given data would be [tex]\sqrt{225}=15[/tex].
[tex]z=\frac{x-62}{25}[/tex]
We know that top 25% means 75% and more.
Let us find z-score corresponding to 75% or 0.75 using normal distribution table.
[tex]0.68=\frac{x-62}{25}[/tex]
Let us solve for x.
[tex]0.68*25=\frac{x-62}{25}*25[/tex]
[tex]17=x-62[/tex]
[tex]17+62=x-62+62[/tex]
[tex]79=x[/tex]
Therefore, 79 marks are required to get a B or higher.
