Standard Deviation of the Mean

What is the 50% error of the mean for the angles observed below?

Trial Angle
A 42º 52′ 09"
B 42º 53′ 11"
C 42º 52′ 28"
D 42º 52′ 31"
E 42º 52′ 22"
F 42º 53′ 05"
Express your answer to three significant figures.

View Available Hint(s)

E50=±
E 50 = ±

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sec

the Standard deviation for the angles is 0.00766°

Step-by-step explanation:

We first covert the angles to standard angle format.

For A) 42° 52' 09'' we have;

42 + (52/60) + (9/3600)

= 42 + 0.866 + 0.00305 = 42.8685°

Repeating the same procedure for the other angles we have

B) 42. 88605°

C) 42.87377°

D) 42.87461°

E) 42.87211°

F) 42.88438°

Mean of the angles becomes

x' = (42.8685+42.88605+42.87377+42.87461+42.87211+42.88448)/6

x' = 42.87657°

x - x' = 0.00807, 0.00948, 0.0028, 0.00196, 0.00446, 0.00781

NB: x - x' values is the mean angle minus the individual angle. We ignore the minus signs

(x - x') ^2 = 0.000065, 0.0000898, 0.0000784, 0.0000384, 0.0000198, 0.0000609

Variance = ( 0.000065+0.0000898+0.0000784+0.0000384+0.0000198+0.0000609)/6

= 0.000358/6 = 0.0000587.

Standard deviation = square root of variance

SD = 0.0000587^0.5 = 0.00766°

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

41*67/2=1373.5

step-by-step explanation:

i just used a calculator