Answer: 0.0001
Step-by-step explanation:
Given : For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1.
i.e. ![\mu=114.8\ \ \ \&\ \ \sigma=13.1](https://tex.z-dn.net/?f=%5Cmu%3D114.8%5C%20%5C%20%5C%20%5C%26%5C%20%5C%20%5Csigma%3D13.1)
Sample size =4
Let x be the sample mean systolic blood pressure.
Then the probability that their mean systolic blood pressure is greater than 140 will be
![P(x>140)=1-P(x\leq140)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{140-114.8}{\dfrac{13.1}{\sqrt{4}}})\\\\\ =1-P(z\leq3.85)\ \ [\because \ z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9999\ \ \text{[By z-table]}\\\\= 0.0001](https://tex.z-dn.net/?f=P%28x%3E140%29%3D1-P%28x%5Cleq140%29%5C%5C%5C%5C%3D1-P%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%5Cleq%5Cdfrac%7B140-114.8%7D%7B%5Cdfrac%7B13.1%7D%7B%5Csqrt%7B4%7D%7D%7D%29%5C%5C%5C%5C%5C%20%3D1-P%28z%5Cleq3.85%29%5C%20%5C%20%5B%5Cbecause%20%5C%20z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%5D%5C%5C%5C%5C%3D1-0.9999%5C%20%5C%20%5Ctext%7B%5BBy%20z-table%5D%7D%5C%5C%5C%5C%3D%200.0001)
Hence, the required probability = 0.0001
Answer:
125/96
Step-by-step explanation:
Multiply 3/8 and 2/3 by common denominator
9/24 + 16/24 = 25/24
Then divide by 4/5 (Multiply by reciprocal)
25/24 * 5/4 = 125/96
.......,.......The answer is B
Answer:
The graph is shown below.
Step-by-step explanation:
Given:
Slope of the line is, ![m=-\frac{2}{3}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B2%7D%7B3%7D)
A point on the line is (-2,2).
Let us find the equation of a line using the point-slope form:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Here, ![x_1=-2,y_1=2,m=-\frac{2}{3}](https://tex.z-dn.net/?f=x_1%3D-2%2Cy_1%3D2%2Cm%3D-%5Cfrac%7B2%7D%7B3%7D)
![y-2=-\frac{2}{3}(x-(-2))\\y-2=-\frac{2}{3}(x+2)\\3(y-2)=-2(x+2)\\3y-6=-2x-4\\2x+3y=-4+6\\2x+3y=2](https://tex.z-dn.net/?f=y-2%3D-%5Cfrac%7B2%7D%7B3%7D%28x-%28-2%29%29%5C%5Cy-2%3D-%5Cfrac%7B2%7D%7B3%7D%28x%2B2%29%5C%5C3%28y-2%29%3D-2%28x%2B2%29%5C%5C3y-6%3D-2x-4%5C%5C2x%2B3y%3D-4%2B6%5C%5C2x%2B3y%3D2)
Let
, then
. So, a point is (1,0).
Another point is given as (-2,2)
Now, draw a line passing through these two points. This is the graph of the required line.