A point located at (-5, -6) is reflected over the y-axis. What are the coordinates of the image? (-5, 6) (5, -6) (5, 6) (-6, -5)
1 answer:
<u>Answer:</u>
The correct answer option is (5, -6).
<u>Step-by-step explanation:</u>
We know that the following are the coordinates of a point:
If this point is reflected through y axis, we are to find the coordinates of its image?
If a point is reflected through y-axis, the sign of the x coordinate is changed so we get:
(5, -6)
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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.