A professor finds that the grades in a large class are normally distributed. The mean of the grades is 64, and the standard deviation is 10.
a.) If 50 students were in the class, how many of them obtained a score between 58 to 70?
a.) If 50 students were in the class, how many of them obtained a score between 58 to 70?
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Answer:
Sample mean=population mean=75
Sample std. dev.= 15/(square root of 10)=4.74
Transforming variable 80 to std.normal distribution, we have
(80-75)/4.74=1.05
Probability that sample mean is greater than 80= 0.5 - P (1.05)=0.5-0.353=0.147
So the required probability = 0.147