The two-way table shows the number of hours of sleep each of 120 student volunteers reported and their exam results.
a) Find P(passing test given <6 hours sleep)
no table?
To find P(passing test given <6 hours sleep) from the given two-way table, you need to calculate the conditional probability.
First, locate the row that represents students who had less than 6 hours of sleep. In this case, it would be the row with "<6 hours sleep" label.
Next, find the column that represents students who passed the test. In this case, it would be the column with "Passed" label.
Now, find the value at the intersection of the row and column. This value represents the number of students who had less than 6 hours of sleep and passed the test.
Finally, divide this value by the total number of students who had less than 6 hours of sleep to get the conditional probability.
Let's assume the value at the intersection is 20 and the total number of students with <6 hours sleep is 40, then the calculation would be:
P(passing test given <6 hours sleep) = 20/40
Simplifying this, you get:
P(passing test given <6 hours sleep) = 1/2
So, the probability of passing the test given less than 6 hours of sleep is 1/2.