)) What time does the clock show?
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The irrational numbers among these given are:
The remaining numbers are all rational.
<h3>What are rational and irrational numbers?</h3>- Rational numbers are numbers that can be represented by fractions, such as terminating decimals.
- Irrational numbers are numbers that cannot be represented by fractions, such as non-terminating decimals and non-exact roots.
The irrational numbers in this problem are:
- Square root of 83, as it is a non-exact root.
- 24π, as π is a non-terminating decimal.
- 90.790170, which is a non-terminating decimal.
- Square root of 109, as it is a non-exact root.
More can be learned about rational and irrational numbers at brainly.com/question/17232771
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Answer:
100% probability that the sample mean weight of these 100 bags is less than 18.6 ounces
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.
In this question, we have that:
What is the probability that the sample mean weight of these 100 bags is less than 18.6 ounces
This is the pvalue of Z when X = 18.6. So
By the Central Limit Theorem
has a pvalue of 1
100% probability that the sample mean weight of these 100 bags is less than 18.6 ounces