(Photo)
2 answers:
Answer: The correct options is (D) 128 units³.
Step-by-step explanation: We are given to find the volume of the regular pyramid shown in the figure.
The VOLUME of a regular pyramid with base area 'b' square units and height 'h' units is given by
In the given figure, we have
base area = 8 × 8 = 64 units² and height, h = 6 units.
Therefore, the volume of the regular pyramid is
Thus, the required volume is 128 units³.
Option (D) is correct.
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Answer:
99.99% probability that the mean weight of a 50-box case of crackers is above 16 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 problem, we have that:
What is the probability that the mean weight of a 50-box case of crackers is above 16 ounces?
This is 1 subtracted by the pvalue of Z when X = 16. So
By the Central Limit Theorem
has a pvalue of 0.0001
1 - 0.0001 = 0.9999
99.99% probability that the mean weight of a 50-box case of crackers is above 16 ounces