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kiruha [24]
3 years ago
14

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 7.9 9.7 9.7 8.7 7.0 7.2 11.3 11.

8 7.3 8.1 8.0 11.6 6.8 9.0 6.3 7.0 7.4 8.7 6.8 5.8 7.8 7.7 6.3 7.0 7.7 6.5 10.7 (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Σxi = 219.8.] (Round your answer to three decimal places.) MPa
Mathematics
1 answer:
dybincka [34]3 years ago
5 0

Answer:

\sum X_i = 219.8

And we can calculate the mean with the following formula:

\bar X = \frac{\sum_{i=1}^n X_i}{n}= \frac{219.8}{27}= 8.141

We can calculate the sample variance with this formula:

s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}= 2.819

And the sample deviation would be given by:

s= \sqrt{s^2}=\sqrt{2.819}= 1.679

Step-by-step explanation:

For this case we have the following data given:

7.9 9.7 9.7 8.7 7.0 7.2 11.3 11.8 7.3 8.1 8.0 11.6 6.8 9.0 6.3 7.0 7.4 8.7 6.8 5.8 7.8 7.7 6.3 7.0 7.7 6.5 10.7

Our variable of interest is given by X="flexural strength (MPa) for concrete beams of a certain type"

And for this case we know that \sum X_i = 219.8

And we can calculate the mean with the following formula:

\bar X = \frac{\sum_{i=1}^n X_i}{n}= \frac{219.8}{27}= 8.141

We can calculate the sample variance with this formula:

s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}= 2.819

And the sample deviation would be given by:

s= \sqrt{s^2}=\sqrt{2.819}= 1.679

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