SOLUTION: The average GPA scored by a class is 4.91 and standard deviation is 0.72. For a sample of 30 students, find the probability that they will have an average GPA between 4.75 and 4.95

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Question 1194410: The average GPA scored by a class is 4.91 and standard deviation is 0.72. For a sample of 30 students, find the probability that they will have an average GPA between 4.75 and 4.95.
Answer by amarjeeth123(569) (Show Source):
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Population Mean mu=4.91
Population Standard Deviation sigma=0.72
Sample size n=30
We have to find the probability that they will have an average GPA between 4.75 and 4.95.
For a normal distribution z=(x-mu)/(sigma/sqrt(n)) where n is the sample size.
x1=4.75
z(lower)=(x1-mu)/(sigma/sqrt(n))=(4.75-4.91)/(0.72/sqrt(30))=−1.22
x2=4.95
z(upper)=(x2-mu)/(sigma/sqrt(n))=(4.95-4.91)/(0.72/sqrt(30))=0.3
The required probability=P(z(lower =0.6195-0.1118=0.5078
Answer:
The required probability=0.5078