Diagram for 19x50 Right answers only
1 answer:
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Answer:
Grades between 62 and 64 result in a D grade.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Find the numerical limits for a D grade.
D: Scores below the top 84% and above the bottom 10%
So below the 100-84 = 16th percentile and above the 10th percentile.
16th percentile:
This is the value of X when Z has a pvalue of 0.16. So X when Z = -0.995.
10th percentile:
This is the value of X when Z has a pvalue of 0.1. So X when Z = -1.28.
Grades between 62 and 64 result in a D grade.
Given:
The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation
To find:
The maximum amount of profit the company can make, to the nearest dollar.
Solution:
If a quadratic equation is , then the vertex is
If a>0, then vertex is the minimum point and if a<0, then the vertex is the maximum point.
We have,
Here, . Clearly, a<0. So, the vertex is the point of maxima.
Putting x=23.931 in the given equation, we get
The vertex is at (23.931,6568.138).
Therefore, the maximum profit is $6568.138 when x=23.931.