Answer: 0.8238
Step-by-step explanation:
Given : Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with
and
.
Let x denotes the scores on a certain intelligence test for children between ages 13 and 15 years.
Then, the proportion of children aged 13 to 15 years old have scores on this test above 92 will be :-
![P(x>92)=1-P(x\leq92)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{92-106}{15})\\\\=1-P(z\leq })\\\\=1-P(z\leq-0.93)=1-(1-P(z\leq0.93))\ \ [\because\ P(Z\leq -z)=1-P(Z\leq z)]\\\\=P(z\leq0.93)=0.8238\ \ [\text{By using z-value table.}]](https://tex.z-dn.net/?f=P%28x%3E92%29%3D1-P%28x%5Cleq92%29%5C%5C%5C%5C%3D1-P%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5Cleq%5Cdfrac%7B92-106%7D%7B15%7D%29%5C%5C%5C%5C%3D1-P%28z%5Cleq%20%7D%29%5C%5C%5C%5C%3D1-P%28z%5Cleq-0.93%29%3D1-%281-P%28z%5Cleq0.93%29%29%5C%20%5C%20%5B%5Cbecause%5C%20P%28Z%5Cleq%20-z%29%3D1-P%28Z%5Cleq%20z%29%5D%5C%5C%5C%5C%3DP%28z%5Cleq0.93%29%3D0.8238%5C%20%5C%20%5B%5Ctext%7BBy%20using%20z-value%20table.%7D%5D)
Hence, the proportion of children aged 13 to 15 years old have scores on this test above 92 = 0.8238
<u>Answer:</u>
![y = -\frac{2}{3}x + 490](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B2%7D%7B3%7Dx%20%2B%20490)
gradient = = ![-\frac{2}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B3%7D)
y-intercept = ![490](https://tex.z-dn.net/?f=490)
<u>Step-by-step explanation:</u>
• The slope-intercept form of an equation takes the general form:
,
where:
m = slope,
c = y-intercept.
• We are given the equation:
![2x + 3y = 1470](https://tex.z-dn.net/?f=2x%20%2B%203y%20%3D%201470)
To change this into the slope-intercept form, we must make y the subject:
[subtract
from both sides]
⇒
[divide both sides by 3]
⇒ ![y = -\frac{2}{3}x + 490](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B2%7D%7B3%7Dx%20%2B%20490)
• Comparing this equation with the general form equation, we see that:
m = ![-\frac{2}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B3%7D)
c =
.
This means that the gradient is
, and the y-intercept is
.
12x+30+4
12x+34
This is 12x + 34 because when we combine all like terms, we get it.
Answer:
It looks like you cut off part of the questions...
Step-by-step explanation: