we know that
Any function f(x) is continuous at x=a only if
We can see that this curve is smooth everywhere except at x=3
so, we will check continuity at x=3
Left limit is:
Right limit is:
Functional value:
we can see that left limit is not equal to right limit
so, limit does not not exist
so, this function is discontinuous at x=3
Since, limit does not exist
so, there will be non-removal discontinuity at x=3
so, option-C........Answer
Answer:
P-value is less than 0.999995 .
Step-by-step explanation:
We are given that a driver's education course compared 1,500 students who had not taken the course with 1,850 students who had.
Null Hypothesis, :
{means students who took the driver's education course and those who didn't took have same chances to pass the written driver's exam the first time}
Alternate Hypothesis, :
{means students who took the driver's education course were more likely to pass the written driver's exam the first time}
The test statistics used here will be two sample Binomial statistics i.e.;
~ N(0,1)
Here, = No. of students passed the exam ÷ No.of Students that had taken the course
=
Similarly,
=
= 1,850
= 1,500
Test Statistics = = -27.38
P-value is given by, P(Z > -27.38) = 1 - P(Z > 27.38)
Now, in z table the highest critical value given is 4.4172 which corresponds to the probability value of 0.0005%. Since our test statistics is way higher than this so we can only say that the p-value for an appropriate hypothesis test is less than 0.999995 .