Locate 11/3 on a number line
2 answers:
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Answer:
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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 question, we have that:
What is the probability that the mean of this sample is less than 15.99 ounces of water?
This is the pvalue of Z when X = 15.99. So
By the Central Limit Theorem
has a pvalue of 0.0179
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
Answer:
About 3 years Speedy Jet printers be guaranteed.
Step-by-step explanation:
Given : Quality control studies for Speedy Jet Computer Printers show the lifetime of the printer follows a normal distribution with
mean and standard deviation
If the company wishes to replace no more than 10% of the printers.
To find : How long should Speedy Jet printers be guaranteed ?
Solution :
Using Z- table,
Z value corresponding to 10% or 0.10 = -1.28.
Applying z-score formula,
The value of x is given by,
Substitute the values,
So, approx 3 years.
Therefore, About 3 years Speedy Jet printers be guaranteed.
Answer:
Step-by-step explanation:
Hello, I think I can help you with this.
According to the information provided in the problem, the area of a trapezoid is given by
Step 1
solve for a, it means isolate a
Have a good day.