Question

The number of classes taken by students per semester at fake college follows the below distribution for a randomly selected student: number of classes 1 2 3 4 5 6 probability 0.06 0.14 0.12 4k 3k 0.19 where k is an unknown value. find the probability that a randomly selected student takes 4 or less classes.

a. 0.4900
b. 0.6000
c. 0.2800
d. 0.5100
e. 0.0700

Answer 1

To find the probability that a randomly selected student takes 4 or fewer classes, sum up the probabilities for each number of classes from 1 to 4. The probability is 0.49 (option a).

Step-by-step explanation:

To find the probability that a randomly selected student takes 4 or fewer classes, we need to sum up the probabilities for each number of classes from 1 to 4.

The given probability distribution tells us that the probability for taking 1, 2, 3, and 4 classes is 0.06, 0.14, 0.12, and 4k respectively.
We are also told that the probabilities for taking 5 and 6 classes are 3k and 0.19 respectively.

Since the total probability must add up to 1, we can set up the following equation:
0.06 + 0.14 + 0.12 + 4k + 3k + 0.19 = 1.
Simplifying the equation gives us 7k + 0.51 = 1.
Subtracting 0.51 from both sides and dividing by 7, we find that k = 0.07.

Now we can find the probability of taking 4 or fewer classes:

0.06 + 0.14 + 0.12 + 4(0.07) = 0.49.

Therefore, the probability that a randomly selected student takes 4 or less classes is 0.49 (option a).