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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:
SAA theorem
Step-by-step explanation:
The given data with regards to ΔLET and ΔPVC are;
ET ≅ VC
∠L ≅ ∠P
∠E ≅ ∠V
From the given relationship, we have that two angles and the adjacent (nonincluded) side to the two angles in ΔLET are congruent to the corresponding two angles and adjacent (nonincluded) side of ΔPVC
Therefore, the congruence theorem that can be used to prove that the two triangles are congruent is the Side-Angle-Angle (SAA) congruency theorem
The SAA congruency theorem states that, two triangles that have two angles and a nonincluded side on one triangle being congruent to the corresponding two angles and a non included side on the other triangle, then the two triangles are congruent.
