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Xghoued2056
24.05.2021 •
Mathematics
To assess the accuracy of a laboratory scale, a reference weight known to weigh exactly 10 grams (g) is weighed repeatedly. The scale readings are Normally distributed with standard deviation sigma = 0.0002 g. The reference weight is weighed 5 times on that scale. The mean result is 10.002} g.
a) Do the 5 weighings give good evidence that the scale is not well calibrated (that is. its mean mu for weighing this weight it not 10 g)?
b) Give a 95% confidence interval for the mean weight on this scale for all possible measurements of the reference weight. What do you conclude about the calibration of this scale?
c) Compare your results in pans (a) and (b). Explain why the confidence interval is more informative than the test result.
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Ответ:
1.) Yes,
2.) (10.0017518 ; 10.0022482)
Step-by-step explanation:
1.) Since the average is > mean, then it shows that scale isn't well calibrated.
2.)
Sample mean = 10.002
Standard Error = σ/√n = 0.0002/√5
df = n - 1 = 5 - 1 = 4
Tcritical(0.05, 4) = 2.776
Margin of Error = Tcritical * standard error
Margin of Error = 2.776*0.0002/√5 = 0.0002482
Confidence interval :
Mean ± margin of error
Lower boundary = 10.002 - 0.0002482 = 10.0017518
Upper boundary = 10.002 + 0.0002482 = 10.0022482
(10.0017518 ; 10.0022482)
C.)
Since 10 does not fall within the interval ; then we can agree with our assertion in (1).
Confidence interval gives a range of of all possible values and not just a single point value.
Ответ:
he sum of the measures of two complementary angles is 90 degrees
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
In this problem we have that
m∠ABD and m∠DBC are complementary
so
m∠ABD + m∠DBC=90° > by complementary angles
and
(m∠ABD + m∠DBC)+m∠EBC=180° > by a linear pair
Find the measure of angle EBC
substitute the given values
(90°)+m∠EBC=180°
∠EBC=180°-90°=90°