The longest side of an acute isosceles triangle is 12 centimeters. Rounded to the nearest tenth, what is the smallest possible l
2 answers:
Answer:
The smallest possible length would be 8.5 cm.
Step-by-step explanation:
Since, an acute isosceles triangle having two congruent sides with three acute interior angles,
Given,
The longest side of an acute isosceles triangle is 12 centimeters,
Let x be the side length of the each of the congruent sides,
So, by the property of acute isosceles triangle,
Hence, the smallest possible length of one of the two congruent sides is 8.5 cm
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Answer:
73.3% probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 8-ounce jars by the mean of a random sample of 100 jars, will be at most 0.02 ounce
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theore.
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.
In this question, we have that:
What is the probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 8-ounce jars by the mean of a random sample of 100 jars, will be at most 0.02 ounce
That is, probability of the sample mean between 8.2-0.02 = 8.18 and 8.2 + 0.02 = 8.22, which is the pvalue of Z when X = 8.22 subtracted by the pvalue of Z when X = 8.18.
X = 8.22
By the Central Limit Theorem
has a pvalue of 0.8665.
X = 8.18
has a pvalue of 0.1335.
0.8665 - 0.1335 = 0.7330
73.3% probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 8-ounce jars by the mean of a random sample of 100 jars, will be at most 0.02 ounce