If the graph of the function is y=x^2 is translated so it’s vertex is now at the point (0,-3), which equation represents the new
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Answer:
92.65% probability that the total weight in a random sample of 47 American adults exceeds 7500 pounds in 2005.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For sums the theorem can also be used, with mean and standard deviation
In this problem, we have that:
Use this information to estimate the probability that the total weight in a random sample of 47 American adults exceeds 7500 pounds in 2005.
This is 1 subtracted by the pvalue of Z when X = 7500. So
By the Central Limit Theorem
has a pvalue of 0.0735
1 - 0.0735 = 0.9265
92.65% probability that the total weight in a random sample of 47 American adults exceeds 7500 pounds in 2005.
Answer:
<em>f(-5)=149603</em>
Step-by-step explanation:
<u>Synthetic Substitution</u>
It's a method to find the value of a polynomial for a given value of x. The polynomial we want to evaluate is
at x=-5
We can, of course, just replace x for -5 and compute the powers, products and sums and subtractions, but we can use the synthetic substitution to avoid the powers, just by multiplying and adding or subtracting. The method requires us to use only the coefficients of the ordered and complete polynomial as shown:
-1 4 -4 -6 -3 -6 -1 -2
Now we set up an arrangement where we can place some operations
-1 4 -4 -6 -3 -6 -1 -2
-5
The second row and a new third row will be filled by computing values as explained below.
The first value of the third row is the very same first coefficient (-1)
-1 4 -4 -6 -3 -6 -1 -2
-5
-1
The second value of the second row is the -5 times the first value of the third row: (-5)(-1)=5
Next value of the third row is the sum of the values above of it: 4+5=9
-1 4 -4 -6 -3 -6 -1 -2
-5 5
-1 9
Now we proceed the same with next values to get the full arrangement or synthetic substitution
-1 4 -4 -6 -3 -6 -1 -2
-5 5 -45 245 -1195 5990 -29920 149605
-1 9 -49 239 -1198 5984 -29921 149603
The very last value of the third row is the required substitution
f(-5)=149603
The formatted table can be seen in the image below
