What is the solution to the equation 3 sqrt (5x-4) = 3 sqrt (7x+8) ? x = –6 x = –1 x = 1 x = 2
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Answer:
0.9544 = 95.44% probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons.
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 normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, 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.
Suppose the mean fill for the shipment is actually 50 gallons. Standard deviation of 0.6 gallons.
This means that
Sample of 100:
This means that
What is the probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons?
This is the pvalue of Z when X = 50.12 subtracted by the pvalue of Z when X = 49.88. So
X = 50.12
By the Central Limit Theorem
has a pvalue of 0.9772
X = 49.88
has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons.
Solution:
we are given that
In the library at Lenape Elementary School, there are 3/8 as many fiction books as there are nonfiction books.
There are 44 books in the school library.
we have been asked to find How many books are fiction books?
Let there are x non fiction books in the library. Then there will be fiction books.
Hence we can write
Hence there are 32 non-fiction books in the library.
and 44-32=12 fiction books in the library.