For the rectangle find the coordinates of p without using any new variable
2 answers:
Answer: The correct option is (2) (a, b).
Step-by-step explanation: We are given to find the co-ordinates of the point 'P' for the rectangle shown in the figure without using any new variable.
Since we are dealing with a rectangle, so each of its angle is a right angle. Hence, each side of the given rectangle is perpendicular to its adjacent side.
Also, the distance of a point from a line is the length of the perpendicular drawn from the point to the line.
So, we can see from the attached figure below that
Point 'P is at a distance of 'b' units from X-axis and 'a' units from Y-axis.
The distance of a point 'P' from Y-axis is its x co-ordinate the distance of 'P' from X-axis is its y co-ordinate.
Therefore, the co-ordinates of the point P will be
(distance of P from Y-axis, distance of P from X-axis)
= (a, b).
Thus, the correct option is (2) (a, b).
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Answer:
The probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 80 employees will be at most $75 is 0.9297.
Step-by-step explanation:
According to the Central Limit Theorem if we have a non-normal population with mean <em>μ</em> and standard deviation <em>σ</em> and appropriately huge random samples (<em>n</em> > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the distribution of sample means is given by,
And the standard deviation of the distribution of sample means is given by,
The information provided is:
As <em>n</em> = 80 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean weekly salaries.
Let represent the sample mean weekly salaries.
The distribution of is:
Now we need to compute the probability of the sampling error made in estimating the mean weekly salary to be at most $75.
The sampling error is the the difference between the estimated value of the parameter and the actual value of the parameter, i.e. in this case the sampling error is, .
Compute the probability as follows:
Thus, the probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 80 employees will be at most $75 is 0.9297.