The high school athletics department is installing a new rectangular addition to their current practice field. the length of the
1 answer:
The system of inequalities that best describes this situation provided A represents the area in which the entire field exists:
Word problems in mathematics exist methods we can utilize variables, algebra notations, and arithmetic operations to solve real-life cases.
We have a new addition to the current rectangular field,
Let that new addition to the current rectangular field be x
Length of the new addition = 10x
Twice the width of the new addition = 2x²
Original area of the field = 300
From the above information, we can derive a quadratic equation:
2x² + 10x + 300
Also, we exist given a constraint that the total area of the practice field should be no more than 1200.
It can be less than 1200 or equivalent to 1200.
Therefore, the system of inequalities that best describes this situation provided A represents the area in which the entire field exists:
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Answer:
99% of the sample means will fall between 0.93288 and 0.94112.
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.
The true mean is .9370 with a standard deviation of 0.0090
This means that
Sample of 32:
This means that
Within what interval will 99 percent of the sample means fall?
Between the 50 - (99/2) = 0.5th percentile and the 50 + (99/2) = 99.5th percentile.
0.5th percentile:
X when Z has a pvalue of 0.005. So X when Z = -2.575.
By the Central Limit Theorem
99.5th percentile:
X when Z has a pvalue of 0.995. So X when Z = 2.575.
99% of the sample means will fall between 0.93288 and 0.94112.