A recipe requires 1/2 cup of sugar for every batch of cakes. How batches of cakes can be made with 5 1/2 cups of sugar?
2 answers:
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Answer:
0.227 = 22.7% probability that the mean printing speed of the sample is greater than 18.12 ppm.
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.
Mean of 17.42 ppm and a standard deviation of 3.25 ppm.
This means that
Sample of 12:
This means that
Find the probability that the mean printing speed of the sample is greater than 18.12 ppm.
This is 1 subtracted by the p-value of Z when X = 18.12.
By the Central Limit Theorem
has a pvalue of 0.773.
1 - 0.773 = 0.227
0.227 = 22.7% probability that the mean printing speed of the sample is greater than 18.12 ppm.
Given:
The inequality is:
To find:
The domain and range of the given inequality.
Solution:
We have,
The related equation is:
This equation is defined if:
In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set. Thus, -3 is not included in the domain.
So, the domain of the given inequality is x>-3.
We know that,
The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.
So, the domain of the given inequality is y>1.
Therefore, the correct option is A.
Answer:
Step-by-step explanation:
- Original equation:
- Subtract 5x from both sides of the equation:
- Divide both sides of the equation by -1:
- Divide both sides of the equation by 3 to get y on the left, leaving the equation in
form:
- Evaluate. Slope is equal to m in this form, so the slope is
.
Hope this helps!