It represents equal parts of a whole or a collection?
2 answers:
You might be interested in
Answer:
10.38% probability that a randomly chosen book is more than 20.2 mm thick
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.
For sums of n elements, the mean is and the standard deviation is
In this problem, we have that:
What is the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers)
This is 1 subtracted by the pvalue of Z when X = 20.2. So
By the Central Limit Theorem
has a pvalue of 0.8962
1 - 0.8962 = 0.1038
10.38% probability that a randomly chosen book is more than 20.2 mm thick
Answer:
The required volume, if he wants to fill 75% of the pot's volume, is 11664cm³
Step-by-step explanation:
The volume of a pyramid is given as
Where V is the pot's volume, A is the base area and h is the height.
Our base is a square, so the base area, if s denotes the side length, would be s x s.
s = 36cm, therefore we have A = 36cm X 36cm = 1296cm².
The height is given as 36cm, therefore we have our volume to be:
Since Luis wants to fill 75% of the pot's volume with soil. Then it will take
Thus, the required volume, if he wants to fill 75% of the pot's volume, is 11664cm³