Respuesta :
For a known standard deviation, the confidence interval for sample size = n is
[tex](x-z \frac{ \sigma }{ \sqrt{n}},x+x \frac{ \sigma }{ \sqrt{n} } )[/tex]
where
x = average
n = sample size
[tex] \sigma [/tex] = stad. deviation
z = contant that reflects confidence interval
Let a = x
Let b = [tex]z \frac{ \sigma }{ \sqrt{n} } [/tex]
From the given information,
a - b = 0.432 (1)
a + b = 0.52 (2)
Add (1) and (2): 2a = 0.952 => a = 0.476
Subtract (2) from (1): -2b = -0.088 => b = 0.044
Therefore, the confidence interval may be written as
(0.476 - 0.044, 0.476 + 0.044), or as
(0.476 [tex] \pm [/tex] 0.044)
[tex](x-z \frac{ \sigma }{ \sqrt{n}},x+x \frac{ \sigma }{ \sqrt{n} } )[/tex]
where
x = average
n = sample size
[tex] \sigma [/tex] = stad. deviation
z = contant that reflects confidence interval
Let a = x
Let b = [tex]z \frac{ \sigma }{ \sqrt{n} } [/tex]
From the given information,
a - b = 0.432 (1)
a + b = 0.52 (2)
Add (1) and (2): 2a = 0.952 => a = 0.476
Subtract (2) from (1): -2b = -0.088 => b = 0.044
Therefore, the confidence interval may be written as
(0.476 - 0.044, 0.476 + 0.044), or as
(0.476 [tex] \pm [/tex] 0.044)
