What is the approximate value for 83 divided 5 ?
2 answers:
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Answer:
The function has been flipped due to the negative in front.
The function has been shifted 17 units to the left.
The function has been shifted 4.3 units down.
Step-by-step explanation:
When functions are transformed there are a few simple rules:
- Adding/subtracting inside the parenthesis to the input shifts the function left(+) and right(-).
- Adding/subtracting outside the parenthesis to the output shifts the function up(+) and down(-).
- Multiplying the function by a number less than 1 compresses it towards the x-axis.
- Multiplying the function by a number greater than 1 stretches it away from the x-axis.
- Multiplying by a negative flips the graph.
The graph of compares to
in the following ways:
The function has been flipped due to the negative in front.
The function has been shifted 17 units to the left.
The function has been shifted 4.3 units down.
Answer:
0.60% probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected
Step-by-step explanation:
To solve this question, we have 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation, which is also called standard error
In this problem, we have that:
The standard deviation is the square root of the variance. So
What is the probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected
Either it differs by 104 or less dollars, or it differs by more than 104 dollars. The sum of the probabilities of these events is 100. I am going to find the probability that it differs by 104 or less dollars first.
Probability that it differs by 104 or less dollars first.
pvalue of Z when X = 16127 + 104 = 16231 subtracted by the pvalue of Z when X = 16127 - 104 = 16023. So
X = 16231
By the Central Limit Theorem
has a pvalue of 0.9970
X = 16023
has a pvalue of 0.0030
0.9970 - 0.0030 = 0.9940
99.40% probability that it differs by 104 or less.
What is the probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected
p + 99.40 = 100
p = 0.60
0.60% probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected
Answer:
Option C.
Step-by-step explanation:
we know that
The area of the shape is equal to the area of the complete rectangle minus the area of the inside square
so