The rectangle ABCD shown on the coordinate plane represents an overhead view of a piece of land. Each until represents 1,000 fee
1 answer:
Assuming the rectangular piece of land is what is given in the image attached below, and each units = 1,000 ft, therefore:
Length = 8,000 ft
Width = 2,000 ft
<h3>Dimensions of a Rectangular Shape</h3>- Rectangular shape has a dimension of length by width.
- On a coordinate plane, the number of units on the longest side of the rectangular shape is the length while the number of units on the shortest side is the width.
Therefore, assuming the rectangular piece of land is what is given in the image attached below, and each units = 1,000 ft, therefore:
- Length = 1,000 ft × 8 units = 8,000 ft
- Width = 1,000 ft × 2 units = 2,000 ft
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Answer:
a) 64.06% probability that he is through grading before the 11:00 P.M. TV news begins.
b) The hardness distribution is not given. But you would have to find s when n = 39, then the probability would be 1 subtracted by the pvalue of Z when X = 51.
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.
For the sum of n trials, the mean is and the standard deviation is
In this question:
These values are in minutes.
(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?
From 6:50 PM to 11 PM there are 4 hours and 10 minutes, so 4*60 + 10 = 250 minutes. This probability is the pvalue of Z when X = 250. So
By the Central Limit Theorem
has a pvalue of 0.6406
64.06% probability that he is through grading before the 11:00 P.M. TV news begins.
(b) What is the (approximate) probability that the sample mean hardness for a random sample of 39 pins is at least 51?
The hardness distribution is not given. But you would have to find s when n = 39(using the standard deviation of the population divided by the square root of 39, since it is not a sum here), then the probability would be 1 subtracted by the pvalue of Z when X = 51.