solve for "l" to find its length
Which two points on the number line are 3 units away from 7?
1 answer:
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solve for "l" to find its length
Answer:
a) 0.27% probability that the mean is less than 1995 milliliters.
b) 2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.
Step-by-step explanation:
To solve this problem, it is important 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
A) If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1995 milliliters?
So
This probability is the pvalue of Z when X = 1995. So
By the Central Limit Theorem
has a pvalue of 0.0027
So 0.27% probability that the mean is less than 1995 milliliters.
B) What mean overfill or more will occur only 10% of the time for the sample of 100 bottles?
This is the value of X when Z has a pvalue of 1-0.1 = 0.9.
So it is X when
2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.
The range is the output of the function, and there are many ways to find it and write it. Let's find it first by plugging in all the domain values (domain means input) into the function:
We have all of our values. We can either write the range as:
{
}
or, subtract the smallest value from the largest one:
So, there are those ways to write it, there are more, but I think you should stick with the first way because that's how the problem was presented to you. If you have any questions, hmu!
We have all of our values. We can either write the range as:
{
or, subtract the smallest value from the largest one:
So, there are those ways to write it, there are more, but I think you should stick with the first way because that's how the problem was presented to you. If you have any questions, hmu!