Suppose that, for a certain exam, a teacher grades on a curve. It is known that the grades follow a normal distribution with a mean of 70 and a standard deviation of 7. There are 45 students in the class. How many students should receive an A? Please, round your answer to the nearest integer

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Describe 3 step to decision making

To determine the number of students who should receive an A on the exam, we need to calculate the z-score corresponding to the A grade cutoff.

The z-score measures how many standard deviations a particular value is away from the mean in a standard normal distribution. In this case, we want to find the z-score for the cutoff point of an A grade.

To calculate the z-score, we use the formula: z = (x - μ) / σ

Where:
- x is the cutoff grade for an A
- μ is the mean of the distribution (70 in our case)
- σ is the standard deviation of the distribution (7 in our case)

The cutoff grade for an A is usually higher than the mean. Let's assume it is 85.

Plugging the values into the formula, we have: z = (85 - 70) / 7 = 2.14

Now, we need to find the proportion of students corresponding to this z-score using a standard normal distribution table or a calculator.

Looking up the z-score of 2.14 in the table or using a calculator, we find that the proportion of students below this z-score is approximately 0.9834.

However, we want to find the number of students who should receive an A, not the proportion. To do that, we need to convert the proportion to actual students.

Multiply the proportion (0.9834) by the total number of students (45):

0.9834 * 45 ≈ 44.256

Rounded to the nearest integer, we find that approximately 44 students should receive an A on the exam.