PLEASE HELP ME I AM STRUGGLING!!!! MATHEMATICS
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Answer:
42.22% probability that the weight is between 31 and 35 pounds
Step-by-step explanation:
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.
In this problem, we have that:
What is the probability that the weight is between 31 and 35 pounds
This is the pvalue of Z when X = 35 subtracted by the pvalue of Z when X = 31. So
X = 35
has a pvalue of 0.5557
X = 31
has a pvalue of 0.1335
0.5557 - 0.1335 = 0.4222
42.22% probability that the weight is between 31 and 35 pounds
I made my own graph using the given points. Pls. see attachment.
<span>Part A: Using the graph above, create a system of inequalities that only contains points D and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.
I used paint program to graph the points based on the given data.
I used a ruler as guide as I draw my line containing both points D and F and extended the line outward.
The yellow lines above represents the shaded portion of the graph.
y = mx + b
b is the y-intercept. It is the value of y when x is 0. In this case, b = 3.5
m is the slope. It is the change in y divided by the change in x.
point D (2,4) ; point F (-2,3)
change in y: 4 - 3 = 1
change in x: 2 - (-2) = 4
m = 1/4
y = 1/4 x + 3.5
Since we are looking for a system of inequality and the portion shaded is in the upper part of the line, the value of y will be greater than or equal to.
y </span>≥ 1/4x + 3.5<span>
Part B: Explain how to verify that the points D and F are solutions to the system of inequalities created in Part A.
To check the solution given above. We will use the x values of points D and F and check whether its y values are equal to or greater than the solution.</span>
y ≥ 1/4x + 3.5
Point D (2,4) : x = 2 : y ≥ 1/4 * 2 + 3.5 → 0.5 + 3.5 → 4
Point F (-2.3): x = -2 ; y ≥ 1/4 * -2 + 3.5 → -0.5 + 3.5 → 3
<span>
Part C: Chickens can only be raised in the area defined by y > 2x − 2. Explain how you can identify farms in which chickens can be raised.
y > 2x - 2
We will get the coordinates of each point and see if its x value will generate the desired value of y.
A(2,-3) ; x = 2 : </span><span>y > 2(2) - 2 </span>→ 4 - 2 → 2 . DID NOT PASS. -3 is lesser than 2.<span>
B(-3,-4) ; x = -3 : y > 2(-3) - 2 </span>→ -6 - 2 → -8. PASSED. -4 is greater than -8.<span>
C(-4,2) ; x = -4 : y > 2(-4) - 2 </span>→ -8 - 2 → -10. PASSED. 2 is greater than -10.<span>
D(2,4) ; x = 2 : y > 2(2) - 2 </span>→ 4 - 2 → 2. PASSED. 4 is greater than 2.<span>
E(3,1) ; x = 3 : y > 2(3) - 2 </span>→ 6 - 2 → 4. DID NOT PASS. 1 is lesser than 4.<span>
F(-2,3) ; x = -2 ; y > 2(-2) - 2 </span>→ -4 - 2 → -6. PASSED. 3 is greater than -6.
Among the farms, points B,C, D, and F can raise chickens based on the given system of linear inequality.
<span>Part A: Using the graph above, create a system of inequalities that only contains points D and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.
I used paint program to graph the points based on the given data.
I used a ruler as guide as I draw my line containing both points D and F and extended the line outward.
The yellow lines above represents the shaded portion of the graph.
y = mx + b
b is the y-intercept. It is the value of y when x is 0. In this case, b = 3.5
m is the slope. It is the change in y divided by the change in x.
point D (2,4) ; point F (-2,3)
change in y: 4 - 3 = 1
change in x: 2 - (-2) = 4
m = 1/4
y = 1/4 x + 3.5
Since we are looking for a system of inequality and the portion shaded is in the upper part of the line, the value of y will be greater than or equal to.
y </span>≥ 1/4x + 3.5<span>
Part B: Explain how to verify that the points D and F are solutions to the system of inequalities created in Part A.
To check the solution given above. We will use the x values of points D and F and check whether its y values are equal to or greater than the solution.</span>
y ≥ 1/4x + 3.5
Point D (2,4) : x = 2 : y ≥ 1/4 * 2 + 3.5 → 0.5 + 3.5 → 4
Point F (-2.3): x = -2 ; y ≥ 1/4 * -2 + 3.5 → -0.5 + 3.5 → 3
<span>
Part C: Chickens can only be raised in the area defined by y > 2x − 2. Explain how you can identify farms in which chickens can be raised.
y > 2x - 2
We will get the coordinates of each point and see if its x value will generate the desired value of y.
A(2,-3) ; x = 2 : </span><span>y > 2(2) - 2 </span>→ 4 - 2 → 2 . DID NOT PASS. -3 is lesser than 2.<span>
B(-3,-4) ; x = -3 : y > 2(-3) - 2 </span>→ -6 - 2 → -8. PASSED. -4 is greater than -8.<span>
C(-4,2) ; x = -4 : y > 2(-4) - 2 </span>→ -8 - 2 → -10. PASSED. 2 is greater than -10.<span>
D(2,4) ; x = 2 : y > 2(2) - 2 </span>→ 4 - 2 → 2. PASSED. 4 is greater than 2.<span>
E(3,1) ; x = 3 : y > 2(3) - 2 </span>→ 6 - 2 → 4. DID NOT PASS. 1 is lesser than 4.<span>
F(-2,3) ; x = -2 ; y > 2(-2) - 2 </span>→ -4 - 2 → -6. PASSED. 3 is greater than -6.
Among the farms, points B,C, D, and F can raise chickens based on the given system of linear inequality.