A rectangular pool is 20 ft wide and 50 ft long. the pool is surrounded by a walkway. the walkway is the same width all the way
1 answer:
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Answer:
0.9544 = 95.44% probability that the sample mean time for reading comic books per week is between 5 and 7 hours.
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 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 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 problem, we have that:
What is the probability that the sample mean time for reading comic books per week is between 5 and 7 hours
This is the pvalue of Z when X = 7 subtracted by the pvalue of Z when X = 5. So
X = 7
By the Central Limit Theorem
has a pvalue of 0.9772
X = 5
has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that the sample mean time for reading comic books per week is between 5 and 7 hours.
Answer:
There are no real values of x for point P to belong to the 4 quadrant
Step-by-step explanation:
<u><em>The question in English is</em></u>
To what real values of x does the point P (3x -6, 2x +4) belong to the 4th quadrant?
we know that
A point in the fourth Quadrant has the x-coordinate positive and the y-coordinate negative
we have the point
P (3x-6, 2x+4)
----> inequality A ( x-coordinate must be positive)
---> inequality B ( y-coordinate must be negative)
Solve Inequality A
-----> (2,∞)
Solve Inequality B
----> (-∞,-2)
The solution of the system is
(-∞,-2) ∩ (2,∞)
therefore
The system has no solution
There are no real values of x for point P to belong to the 4 quadrant