Answer:
To get a B or higher, you need to get a grade of at least 69.77.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by

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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
In this problem, we have that
Mean of 62, so 
Q1 of 52 means that the z score of X = 52 has a pvalue of 0.25. Z has a pvalue of 0.25 between -0.67 and -0.68, so we use 



Multiplying the equality by (-1), we have that:



If the instructor wishes to assign B's or higher to the top 30% of the students in the class, what grade is required to get a B or higher?
Those are the Z scores that have a pvalue higher than 0.70. So we have to find X when Z has a pvalue of 0.70. This is between 0.52 and 0.53, so we use 




To get a B or higher, you need to get a grade of at least 69.77.