Solution: The sample mean of sample 1 is:
The sample mean of sample 2 is:
The sample mean of sample 3 is:
The sample mean of sample 4 is:
The minimum sample mean of the four sample means is 3.6 and maximum sample mean of the four sample means is 4.4.
Therefore, using his four samples, between 3.6 and 4.4 will Ardem's actual population mean lie.
Hence the option 3.6 and 4.4 is correct
In these questions, we need to follow the steps:
1 - solve for the trigonometric function
2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.
3 - Complete these angles with the complete round repetition, by adding
4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for <em>x</em> to get the solutions.
1 - To solve, we just use algebraic operations:
2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:
The value for the angle that give positive
is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of
Are:
3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:
Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:
4 - Now, we need to solve for <em>x</em>, because these solutions are for all the interior of the tangent function, so:
So, the solutions are:
