The probabilities that a student will attain a 3.6 GPA, at least a 3.0 GPA, at least a 2.5 GPA,

step 1 The phrase at least means greater than equal to, and you use subtraction and complements. So we'

The probabilities that a student will attain a 3.6 GPA, at...

The probabilities that a student will attain a $3.6 \mathrm{GPA}$, at least a $3.0 \mathrm{GPA}$, at least a $2.5 \mathrm{GPA}$, and at least a $2.0 \mathrm{GPA}$ are $.08, .47, .69$, and $.81$, respectively. Find the probabilities associated with each of the following. a. A GPA worse than $3.0$ but greater than $2.5$ b. A GPA worse than $2.0$ c. A GPA of at least $2.5$ d. A GPA worse than $3.0$

The probabilities that a student will attain a $3.6 \mathrm{GPA}$, at least a $3.0 \mathrm{GPA}$, at least a $2.5 \mathrm{GPA}$, and at least a $2.0 \mathrm{GPA}$ are $.08, .47, .69$, and $.81$, respectively. Find the probabilities associated with each of the following.
a. A GPA worse than $3.0$ but greater than $2.5$
b. A GPA worse than $2.0$
c. A GPA of at least $2.5$
d. A GPA worse than $3.0$

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Key Concepts

Cumulative Distribution

A cumulative distribution provides the probability that a variable is less than or equal to a specific value or, in some cases, at least a specific value. Understanding cumulative distributions is important when dealing with 'at least' or 'worse than' probability statements, as it allows for direct usage or subtraction to find the desired probabilities.

Interval Probabilities

Interval probabilities involve computing the probability that a random variable falls within a specific range. This is typically done by taking the difference between cumulative probabilities at two cutoff points, which is essential when calculating the likelihood of a GPA lying between two specified values.

Complement Rule

The complement rule states that the probability of the complement of an event is equal to one minus the probability of the event. This rule is crucial when determining the probability of events such as 'worse than a certain GPA' by subtracting the probability of being at or above that GPA from one.

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