The slope is the same as the gradient
y=mx+c where m is the gradient and c is the y intercept
y=-5x-9
Therefore the 'slope' is -5 i.e. it goes down 5 every 1 across.
Using the <em>normal distribution and the central limit theorem</em>, it is found that there is a:
a) 0.1813 = 18.13% probability that a person selected at random will score between 240 and 270 on the test.
b) 0.4501 = 45.01% probability that the mean score for the sample will be between 240 and 270.
<h3>Normal Probability Distribution</h3>
In a normal distribution with mean
and standard deviation
, the z-score of a measure X is given by:

- It 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, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
In this problem:
- The mean is of
.
- The standard deviation is of
.
Item a:
The probability is the <u>p-value of Z when X = 270 subtracted by the p-value of Z when X = 240</u>, hence:
X = 270:



has a p-value of 0.6217.
X = 240:



has a p-value of 0.4404.
0.6217 - 0.4404 = 0.1813.
0.1813 = 18.13% probability that a person selected at random will score between 240 and 270 on the test.
Item b:
We have a sample of 7, hence:

X = 270:

By the Central Limit Theorem



has a p-value of 0.7910.
X = 240:



has a p-value of 0.3409.
0.7910 - 0.3409 = 0.4501.
0.4501 = 45.01% probability that the mean score for the sample will be between 240 and 270.
To learn more about the <em>normal distribution and the central limit theorem</em>, you can check brainly.com/question/24663213
Answer: x = 1 , y = 5
Step-by-step explanation:
Because the focus is (-2,-2) and the directrix is y = -4, the vertex is (-2,-3).
Consider an arbitrary point (x,y) on the parabola.
The square of the distance between the focus and P is
(y+2)² + (x+2)²
The square of the distance from the point to the directrix is
(y+4)²
Therefore
(y+4)² = (y+2)² + (x+2)²
y² + 8y + 16 = y² + 4y + 4 + (x+2)²
4y = (x+2)² - 12
y = (1/4)(x+2)² - 3
Answer: