Respuesta :
Answer:
Grade A: [tex]Z \geq 1[/tex]
Grade B: [tex]0 \leq Z < 1[/tex]
Grade C: [tex]-1 \leq Z < 0[/tex]
Grade D: [tex]Z < -1[/tex]
Step-by-step explanation:
Problems of normally distributed samples can be solved using the Z score table.
The Z score of a measure represents how many standard deviations it is above or below the mean of all the measures.
Each Z score has a pvalue. This represents the percentile of the measure.
In this problem, we have that:
The upper 16% of the class get A grades. The upper 16% has a pvalue of at least 100% = 16% = 84% = 0.84. This is [tex]Z \geq 1[/tex].
The middle 34% of the class get B grades. The middle 34% has a pvalue of at least 84%-35% = 50% = 0.5 and at most 0.84. This is [tex]0\leqZ < 1[/tex].
Those between a pvalue of 0.5-0.34 = 0.16 and 0.5 get get grade C. [tex]Z = -1[/tex] has a pvalue of 0.16. So a grade C is in the interval [tex]-1 \leq Z < 0[/tex].
Those with Z lesser than -1 get grades D and F
