PLz help me! We r doing semester finals and i need to get this lesson finished in 2 hours so i can get my grade up!
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Answer:
a) 20.16; b) 20.49 and 21.51
Step-by-step explanation:
We use z scores for each of these. The formula for a z score is
.
For part a, we want the 20th percentile; this means we want 20% of the data to be lower than this. We find the value in the cells of the z table that are the closest to 0.20 as we can get; this is 0.2005, which corresponds with a z score of -0.84.
Using this, 21 as the mean and 1 as the standard deviation,
-0.84 = (X-21)/1
-0.84 = X-21
Add 21 to each side:
-0.84+21 = X-21+21
20.16 = X
For part b, we want the middle 39%. This means we want 39/2 = 19.5% above the mean and 19.5% below the mean; this means we want
50-19.5 = 30.5% = 0.305 and
50+19.5 = 69.5% = 0.695.
Looking these values up in the cells of the z table, we find those exact values; 0.305 corresponds with z = -0.51 and 0.695 corresponds with z = 0.51:
-0.51 = (X-21)/1
-0.51 = X-21
Add 21 to each side:
-0.51+21 = X-21+21
20.49 = X
0.51 = (X-21)/1
0.51 = X-21
Add 21 to each side:
0.51+21 = X-21+21
21.51 = X
To solve for x, we have to remember to isolate the variable.
For 1/2, we can make that 0.5, since their values are equivalent. Our equation:
Let's distribute the 0.5 first.
Now, let's simplify the right side of the equation. We have to distribute the negative to 3x and 1.
Then, we simplify the entire expression.
Our equation now:
Let's add 3x to the right and 3x to the left to simplify the -3x on the right side of the equation.
Let's do the same thing we did in Step 3 to 1.5. Subtract 1.5 on both sides of the equation.
Finally, we divide both sides by 6 to isolate x.