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3 years ago

Which expression is equivalent to ? A. B. C. D.

Mathematics

2 answers:

Lorico [155]3 years ago

8 0

$\longrightarrow{\green{ D. \: 18 \frac{1}{5} + 22 \frac{2}{5} + 40 \frac{1}{5} }}$

$\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}$

$18 \frac{1}{5} - ( - 22 \frac{2}{5} ) - ( - 40 \frac{1}{5} )\\$

$= 18 \frac{1}{5} + 22 \frac{2}{5} + 40 \frac{1}{5} \\$

( - ) x ( - ) = ( + )

$\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35☂}}}}}$

sweet-ann [11.9K]3 years ago

7 0

The answer is B, A, and D

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(a) A 99% confidence interval for the actual mean noise level in hospitals is (44.02 db, 49.98 db).

(b) We can be 90% confident that the actual mean noise level in hospitals is 47 db with a margin of error of 1.89 db.

(c) Unless our sample (of 81 hospitals) is among the most unusual 2% of samples, the actual mean noise level in hospitals is between 44.41 db and 49.59 db.

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The problem is incomplete. The questions are:

(a) A 99% confidence interval for the actual mean noise level in hospitals is (44.02 db, 49.98 db).

For a 99% CI, the value of z is z=2.58

Then, the confidence interval for the mean is:

$M-z\sigma/\sqrt{n}\leq\mu\leq M-z\sigma/\sqrt{n}\\\\47-2.58*10/\sqrt{75} \leq\mu\leq47+2.58*10/\sqrt{75}\\\\47-2.98\leq\mu\leq47+2.98\\\\44.02\leq\mu\leq 49.98$

(b) We can be 90% confident that the actual mean noise level in hospitals is 47 db with a margin of error of 1.89 db.

For a 90% CI, the value of z is z=1.64.

Then, we can calculate the margin of error as:

$E=z*\sigma/\sqrt{n}=1.64*10/\sqrt{75}=1.89$

(c) Unless our sample (of 81 hospitals) is among the most unusual 2% of samples, the actual mean noise level in hospitals is between 44.41 db and 49.59 db.

The 2% tails data corresponds, in the standard normal distirbution, to the values of z whose absolute value is higher than 2.33.

The values of db for these critical values are:

$X_1=M+z_1*\sigma/\sqrt{n}=47+(-2.33)*10/\sqrt{81}=47-2.59=44.41\\\\\\ X_2=M+z_2*\sigma/\sqrt{n}=47+(2.33)*10/\sqrt{81}=47+2.59=49.59$

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