The table shows the number of hours of sleep all members of a theater group got the night before their musical.
2 answers:
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Answer:
The blood potassium level L such that the probability is only 0.05 that the average of four measurements is less than L is 3.64.
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means of size n can be approximated to a normal distribution with mean
and standard deviation, which is also called standard error
In this problem, we have that:
What is the blood potassium level L such that the probability is only 0.05 that the average of four measurements is less than L?
This is the value of X when Z has a pvalue of 0.05. So it is X when Z = -1.645.
By the Central Limit Theorem
The blood potassium level L such that the probability is only 0.05 that the average of four measurements is less than L is 3.64.
Answer:
We are given that,
The equation of the rainbow is represented by the parabola,
Now, we are required to find a linear equation which cuts the graph of the parabola at two points.
Let us consider the equation joining the points (-6,0) and (0,36), given by .
So, the corresponding table for the linear equation is given by,
x
-6 0
0 36
1 42
6 72
Now, we will answer the questions corresponding the functions.
1. Domain and Range of the rainbow.
Since, the equation of the rainbow is
So, from the figure, we get that,
Domain is the set of all real numbers.
Range is the set
<em>Here, domain represents the points which are used to plot the path of the rainbow and range represents the points which are form the rainbow.</em>
Not all points make sense in the range as the parabola is opening downwards having maximum point as (0,36).
2. X and Y-intercepts of the rainbow.
<em>As, the 'x and y-intercepts are the points where the graph of the function cuts x-axis and y-axis respectively i.e. where y=0 and x=0 receptively'.</em>
We see that from the figure below,
X-intercepts are (-6,0) and (6,0) and the Y-intercept is (0,36)
<em>Here, these intercepts represents the point where the parabola intersects the individual axis.</em>
3. Is the linear function positive or negative.
As the linear function is represented by the <em>upward flight of the drone.</em>
So, the linear function is a positive function.
4. The solution of the system of equations is the intersection points of their graphs.
So, from the figure, we see that the equations intersect at the points (-6,0) and (0,36).
<em>Thus, the solution represents the position when both the drone and rainbow intersect each other.</em>
Answer: I have included an image of the correct answer.
They are skew lines
