For the distribution of GPAs described in problem 1, what is the probability that a randomly selected student will have a GPA Z score Probability
a. less than 3.40
b. less than 3.78
c. more than 3.50
d. more than 2.50
e. between 2.00 and 3.00
f. between 3.00 and 3.50

Question

For the distribution of GPAs described in problem 1, what is the probability that a randomly selected student will have a GPA Z score Probability 
a. less than 3.40 
b. less than 3.78 
c. more than 3.50 
d. more than 2.50 
e. between 2.00 and 3.00 
f. between 3.00 and 3.50

Quizplus · Accepted Answer

To answer these questions, we need to know the mean and standard deviation of the GPA distribution. However, since this information is not provided, I will assume that the GPA distribution follows a standard normal distribution with a mean (?) of 0 and a standard deviation (?) of 1. This is because Z-scores are typically used in the context of a standard normal distribution.
Given this assumption, we can use the standard normal distribution table or a calculator with statistical functions to find the probabilities associated with each Z-score. Here are the probabilities for each scenario:
a. Probability of a Z-score less than 3.40:
The probability of a Z-score less than 3.40 is very close to 1 (or 100%) because 3.40 is far above the mean in a standard normal distribution. Z-scores this high are in the extreme tail of the distribution.
b. Probability of a Z-score less than 3.78:
Similarly, the probability of a Z-score less than 3.78 is also very close to 1, as 3.78 is even further in the tail of the distribution.
c. Probability of a Z-score more than 3.50:
The probability of a Z-score more than 3.50 is very small, close to 0, because it is in the extreme upper tail of the distribution.
d. Probability of a Z-score more than 2.50:
The probability of a Z-score more than 2.50 is also small, as 2.50 is well above the mean, but it is not as extreme as 3.50 or higher Z-scores.
e. Probability of a Z-score between 2.00 and 3.00:
To find this probability, we would calculate the probability of a Z-score less than 3.00 and subtract the probability of a Z-score less than 2.00. Both probabilities are found using the standard normal distribution table or calculator.
f. Probability of a Z-score between 3.00 and 3.50:
This is found in a similar way to part e. Calculate the probability of a Z-score less than 3.50 and subtract the probability of a Z-score less than 3.00.
Please note that without the actual mean and standard deviation of the GPAs, or the specific details of "problem 1" mentioned in your question, I can only provide a general approach based on the assumption of a standard normal distribution. If the GPA distribution is not standard normal, you would need to convert the GPAs to Z-scores using the actual mean and standard deviation of the distribution before finding the probabilities.

For the Distribution of GPAs Described in Problem 1, What