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Answer:
68.26% probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 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 a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds
This is the pvalue of Z when X = 8.6 subtracted by the pvalue of Z when X = 6.4. So
X = 8.6
has a pvalue of 0.8413
X = 6.4
has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
68.26% probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds
<h3>Answer: (2, 2)</h3>
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Explanation:
The phrasing "translated along <4,6>" is another way of saying "shift 4 to the right, shift 6 up"
In general, "translated along <m,n>" is the same as writing . If m is positive, then we shift m units to the right. If m is negative, then we shift to the left. The same story happens with the n, but we focus on the y coordinate.
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With all that in mind, starting at F(-5,-9) and translating along <4,6> has us arrive at (-1, -3). Add 4 to the x coordinate and add 6 to the y coordinate.
We can say
Showing that (-5,-9) moves to (-1,-3)
This is after the first translation, but there's a second translation.
We'll apply the same idea, but different numbers this time
So (-1,-3) moves to (2,2)
Overall we have
- (-5,-9) move to (-1,-3) after the first translation
- (-1,-3) move to (2,2) after the second translation
Therefore, the original point ends up at (2,2) which is the final answer
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Extra info:
A nice shortcut is that the vectors <4,6> and <3,5> can be added to get <4+3,6+5> = <7,11>. So overall, we're shifting 7 units to the right and 11 units up when we combine the two translation vectors.