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Mrs. Simpson’s calculus class has an exam with an average score of 80 and standard deviation of 15. Assume that exam scores are normally distributed. If Mrs. Simpson decides to give an A grade to students who score in the top 20% of the class, what exam score is needed in order to get the A grade? (3pts)

Respuesta :

Answer:

93 is the exam score needed in order to get the A grade in Mrs Simpson’s test

Step-by-step explanation:

Let x be the score that gives an A grade

Mathematically from the z-score formula, we know that;

z-score = x-mean/SD

From the question, x = ? , mean = 80 and SD = 15

Thus;

z-score = x-80/15

But in this question, we have the probability but we do not have the z-score

So we need the z-score that is equivalent to 20%

20% is same as 0.2

Using the standard normal distribution table, a probability of 0.2 corresponds to a z-score of 0.84

Thus, mathematically;

0.84 = x-80/15

x-80 = 15(0.84)

x-80 = 12.6

x = 80 + 12.6

x = 92.6 which is approximately 93

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