This question is incomplete, the complete question is;
Refer to the Exhibit Student Grades. A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11.
The professor has informed the class that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A
Answer:
the minimum score needed to receive a grade of A is 88.51
Step-by-step explanation:
Given the data in the question;
Let x represent the grades of the students that were normally distributed with mean μ = 73 and standard deviation σ = 11.
so, The professor has informed the class that 7.93 percent of her students received grades of A
the minimum score needed to receive a grade of A will be:
P( X > x ) = 7.93 %
P( X > x ) = 0.0793
1 - P( X ≤ x ) = 0.0793
- P( X ≤ x ) = 0.0793 - 1
- P( X ≤ x ) = - 0.9207
P( X ≤ x ) = 0.9207
⇒ P( X-μ/σ ≤ x-μ/σ ) = 0.9207
so, x-μ/σ = InvNormal( 0.9207 )
x-μ/σ = 1.41
(x - 73) / 11 = 1.41
(x - 73) = 1.41 × 11
(x - 73) = 15.51
x = 15.51 + 73
x = 88.51
Therefore, the minimum score needed to receive a grade of A is 88.51
