The GPA of Students at the University has

Tamia Edwards

Tamia Edwards

Answered question

2022-07-07

The GPA of Students at the University has a normal distributed with a mean of 3.62 and a variance of 6.25.

 

a. Calculate the probability that for a randomly select student, the GPA will be more than 3.99.

Answer & Explanation

Andre BalkonE

Andre BalkonE

Skilled2023-05-29Added 110 answers

To calculate the probability that for a randomly selected student, the GPA will be more than 3.99, we can use the properties of the normal distribution.
Given that the GPA of students at the university follows a normal distribution with a mean (μ) of 3.62 and a variance (σ2) of 6.25, we can calculate the probability using the cumulative distribution function (CDF) of the normal distribution.
Let's denote the random variable representing the GPA as X. We are interested in finding P(X>3.99).
First, we need to standardize the value 3.99 using the z-score formula:
z=xμσ
Plugging in the values, we have:
z=3.993.626.25
Simplifying:
z=0.372.5
z=0.148
Now, we can find the probability using the standard normal distribution table or a calculator:
P(X>3.99)=P(Z>0.148)
Using the standard normal distribution table or a calculator, we find that the probability corresponding to a z-value of 0.148 is approximately 0.5596.
Therefore, the probability that for a randomly selected student, the GPA will be more than 3.99 is approximately 0.5596 or 55.96%.

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