Question

asked 2021-05-14

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

\(\begin{array}{|c|c|}\hline 11.8 & 7.7 & 6.5 & 6 .8& 9.7 & 6.8 & 7.3 \\ \hline 7.9 & 9.7 & 8.7 & 8.1 & 8.5 & 6.3 & 7.0 \\ \hline 7.3 & 7.4 & 5.3 & 9.0 & 8.1 & 11.3 & 6.3 \\ \hline 7.2 & 7.7 & 7.8 & 11.6 & 10.7 & 7.0 \\ \hline \end{array}\)

a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. \([Hint.\ ?x_{j}=219.5.]\) (Round your answer to three decimal places.)

MPa

State which estimator you used.

\(x\)

\(p?\)

\(\frac{s}{x}\)

\(s\)

\(\tilde{\chi}\)

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.

\(s\)

\(x\)

\(p?\)

\(\tilde{\chi}\)

\(\frac{s}{x}\)

c) Calculate a point estimate of the population standard deviation ?. \([Hint:\ ?x_{i}2 = 1859.53.]\) (Round your answer to three decimal places.)

MPa

Interpret this point estimate.

This estimate describes the linearity of the data.

This estimate describes the bias of the data.

This estimate describes the spread of the data.

This estimate describes the center of the data.

Which estimator did you use?

\(\tilde{\chi}\)

\(x\)

\(s\)

\(\frac{s}{x}\)

\(p?\)

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 \(\frac{?}{?}\). (Round your answer to four decimal places.)

State which estimator you used.

\(p?\)

\(\tilde{\chi}\)

\(s\)

\(\frac{s}{x}\)

\(x\)

\(\begin{array}{|c|c|}\hline 11.8 & 7.7 & 6.5 & 6 .8& 9.7 & 6.8 & 7.3 \\ \hline 7.9 & 9.7 & 8.7 & 8.1 & 8.5 & 6.3 & 7.0 \\ \hline 7.3 & 7.4 & 5.3 & 9.0 & 8.1 & 11.3 & 6.3 \\ \hline 7.2 & 7.7 & 7.8 & 11.6 & 10.7 & 7.0 \\ \hline \end{array}\)

a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. \([Hint.\ ?x_{j}=219.5.]\) (Round your answer to three decimal places.)

MPa

State which estimator you used.

\(x\)

\(p?\)

\(\frac{s}{x}\)

\(s\)

\(\tilde{\chi}\)

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.

\(s\)

\(x\)

\(p?\)

\(\tilde{\chi}\)

\(\frac{s}{x}\)

c) Calculate a point estimate of the population standard deviation ?. \([Hint:\ ?x_{i}2 = 1859.53.]\) (Round your answer to three decimal places.)

MPa

Interpret this point estimate.

This estimate describes the linearity of the data.

This estimate describes the bias of the data.

This estimate describes the spread of the data.

This estimate describes the center of the data.

Which estimator did you use?

\(\tilde{\chi}\)

\(x\)

\(s\)

\(\frac{s}{x}\)

\(p?\)

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 \(\frac{?}{?}\). (Round your answer to four decimal places.)

State which estimator you used.

\(p?\)

\(\tilde{\chi}\)

\(s\)

\(\frac{s}{x}\)

\(x\)

asked 2021-05-01

Find all zeros of p(x), real or imaginary. \(p(x) = x^{4} + 6x^{3} + 6x^{2} -18x -27\) List all of the possible rational zeros according to the rational zero theorem and state the values for C, A, B and D in the following partial factorization of \(p(x) = (x-c)(x^{3}+Ax^{2}+Bx+D)\) State the exact answer and a decimal approximation of each zero to the tenths place

asked 2021-05-21

The pmf of the amount of memory X (GB) in a purchased flash drive is given as the following.

\(\begin{array}{|c|c|}\hline x & 1 & 2 & 4 & 8 & 16 \\ \hline p(x) & 0.05 & 0.10 & 0.30 & 0.45 & 0.10 \\ \hline \end{array} \)

a) Compute E(X). (Enter your answer to two decimal places.) GB

b) Compute V(X) directly from the definition. (Enter your answer to four decimal places.) \(GB^{2}\)

c) Compute the standard deviation of X. (Round your answer to three decimal places.) GB

d) Compute V(X) using the shortcut formula. (Enter your answer to four decimal places.) \(GB^{2}\)

\(\begin{array}{|c|c|}\hline x & 1 & 2 & 4 & 8 & 16 \\ \hline p(x) & 0.05 & 0.10 & 0.30 & 0.45 & 0.10 \\ \hline \end{array} \)

a) Compute E(X). (Enter your answer to two decimal places.) GB

b) Compute V(X) directly from the definition. (Enter your answer to four decimal places.) \(GB^{2}\)

c) Compute the standard deviation of X. (Round your answer to three decimal places.) GB

d) Compute V(X) using the shortcut formula. (Enter your answer to four decimal places.) \(GB^{2}\)

asked 2021-08-01

\(\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline f(x) & 20 & 21.6 & 29.2 & 36.4 & 46.6 & 55.7 & 72.6 & 87.1 & 107.2 & 138.1 \\ \hline \end{array}\)