a crane cable can support a maximum load of 15,000 kg. if a bucket has a mass of 2,000 kg and gravel has a mass of 1,500 kg for
2 answers:
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Answer:
97.74% probability that the sample mean would differ from the true mean by less than 1.9 dollars if a sample of 92 5-gallon pails is randomly selected
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 random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the sample mean would differ from the true mean by less than 1.9 dollars if a sample of 92 5-gallon pails is randomly selected?
This is the pvalue of Z when X = 29 + 1.9 = 30.9 subtracted by the pvalue of Z when X = 29 - 1.9 = 27.1. So
X = 30.9
By the Central Limit Theorem
has a pvalue of 0.9887
X = 27.1
has a pvalue of 0.0113
0.9887 - 0.0113 = 0.9774
97.74% probability that the sample mean would differ from the true mean by less than 1.9 dollars if a sample of 92 5-gallon pails is randomly selected
Answer:
Step-by-step explanation:
We are given that
Function f decreases from quadrant 2 to quadrant 1 and approaches y=0
It cut the y- axis at (0,6) and passing through the point (1,2).
Function g(x) approaches y=0 in quadrant 2 and increases into quadrant 1.
It passing through the point (-1,2) and cut the y-axis at point (0,6).
Reflection across y- axis:
Rule of transformation is given by
Using the rule then we get
By using
Substitute x=-1
Substitute x=0
Therefore, is true.
