Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 7.4 7.7 9.7 8.1 8.7 6.3 7.8 11.6 9.0 7.7 6.8 7.9 11.3 6.8 8.7 5.8 7.3 7.2 7.8 9.7 7.0 11.8 7.1 10,7 6,5 7.0 6,3 (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Ex, = 219.7.] (Round your answer to three decimal places.) MPa State which estimator you used. O s/X O s (b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%. MPa State which estimator you used. O s/X O s
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
7.4 7.7
9.7 8.1 8.7
6.3 7.8
11.6 9.0
7.7 6.8 7.9
11.3 6.8
8.7 5.8
7.3 7.2 7.8
9.7 7.0
11.8 7.1
10.7 6.5 7.0
6.3
(a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Ex; = 219.7.] (Round your answer to three decimal places.)
MPа
State which estimator you used.
O s/x
(b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%.
MPа
State which estimator you used.
s/X
O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefdfbc0a-81d9-4bf3-a925-5e28ea362bbf%2Fca936d58-c997-42b7-8a7b-3c2125bb3ef9%2Fp0ek108_processed.png&w=3840&q=75)
![(c) Calculate a point estimate of the population standard deviation o. [Hint: Ex, = 1860.87.] (Round your answer to three decimal places.)
MPа
Interpret this point estimate.
O This estimate describes the bias of the data.
This estimate describes the linearity of the data.
This estimate describes the spread of the data.
This estimate describes the center of the data.
Which estimator did you use?
s/ x
(d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)
(e) Calculate a point estimate of the population coefficient of variation o/u. (Round your answer to four decimal places.)
State which estimator you used.
O s/x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefdfbc0a-81d9-4bf3-a925-5e28ea362bbf%2Fca936d58-c997-42b7-8a7b-3c2125bb3ef9%2Fqytgwom_processed.png&w=3840&q=75)
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