Answer:
Step-by-step explanation:
Previous concepts
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
And 0 for other case. Let X the random variable that represent "The number of years a radio functions" and we know that the distribution is given by:
Or equivalently:
Solution to the problem
For this case we are interested in the total T, and we can find the mean and deviation for this like this:
If we solve for T we got:
And the expected value is given by:
And we can find the variance like this:
And then the deviation is given by:
And the distribution for the total is:
And we want to find this probability:
And we can use the z score formula given by:
And replacing we got this:
Answer:
1. Take the Average of the distances the ball travelled each hit.
2. He should use the Interquartile Range. This is the difference between the Upper Quartile and the Lower Quartile of the distances he hits the ball.
3. He should use Mean
4. He should use Median. It best measures skewed data
Step-by-step explanation:
THE FIRST PART.
Raul should take the average of the distances the ball travelled each hit.
This is done by summing the total distances the ball travelled each bounce, and then dividing the resulting value by the total number of times he hit the ball, which is 10.
THE SECOND PART
He should use the Interquartile Range. This is the difference between the Upper Quartile and the Lower Quartile of the distances he hits the ball.
THE THIRD PART
He should take the mean of the distances of the ball that stayed infield.
This is the distance that occurred the most during the 9 bounces that stayed infield. The one that went outfield is makes it unfair to use any other measure of the center, taking the mean will give a value that is significantly below his efforts.
THE FOURTH PART
He should take the Median of the data, it is best for skewed data.
This is the middle value for all the distances he recorded.
Answer:
New Digit = 315,864
Step-by-step explanation:
Given:
Digit - 135,864
Value of digit 3 = 30,000
Find:
New Digit, Value of 3 is 10 times greater
Computation:
Value of 3 is 10 times greater = (30,000) = 300,000
New Digit = 315,864
Answer: 0.7619
Step-by-step explanation:
Given : Mean : 
Standard deviation : 
Sample size : 
We assume that the variable is normally distributed.
The value of z-score is given by :-
a) For x= 46.9 years
The p-value : 
Hence, the probability that the average age of those doctors is less than 46.9 years =0.7619
The right answer is:
<em>area B = area C</em>
We can solve this problem by using Kepler's laws of planetary motion. There are three Kepler's laws. In this exercise, we need to use the second law. According to this law,<em> a line segment joining a planet and the sun sweeps out equals areas during equals intervals of time. </em>So, a certain planet sweeps out an <em>area B </em>from the point <em>P3 </em>to <em>P4</em> in an interval of time <em>t. </em>On the other hand, for the same interval of time <em>t, </em>the planet sweeps out an <em>area C </em>from point <em>P4</em> to <em>P5, </em>that is equal to the previous area according to second kepler's law.
