The minimum score needed to make an A is 89.
<h3>What is the z-score?</h3>
A Z Score, also known as the Standard Score, is a calculation used to determine how many standard deviations a raw score is below or above the population mean. Simply said, the Z Score informs you of a value's relationship to the mean and the distance a data point is from the mean.
Since the grades of his students were normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = grades of his students.
µ = mean grade
σ = standard deviation
From the information given,
µ = 74
σ = 10
The professor has informed us that 6.3 percent of his students received A's. The p-value for the minimum score is 1 - 0.063 = 0.937. The z value of 0.937 is 1.53.
1.53 = (x - 74)/10
1.53 × 10 = x - 74
15.3 = x - 74
x = 15.3 + 74
x = 89.3
Therefore, the minimum score needed to make an A is 89.
The complete question is given below:-
A professor at a local community college noted that the grades of his students were normally distributed with a mean of 74 and a standard deviation of 10. The professor has informed us that 6.3 percent of his students received A's while only 2.5 percent of his students failed the course and received F's. What is the minimum score needed to make an A?
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