Express the confidence interval 172.3<\mu<229.1 in the form of \bar{x}\pm

fortdefruitI 2021-09-30 Answered

Express the confidence interval \(\displaystyle{172.3}{<}\mu{<}{229.1}\) in the form of \(\displaystyle\overline{{{x}}}\pm{M}{E}.\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Dora
Answered 2021-10-01 Author has 17734 answers

Step 1
We know that,
\(\displaystyle\overline{{{X}}}-{M}.{E}.{<}\mu{<}\overline{{{X}}}+{M}.{E}.\)
(1) \(\displaystyle\overline{{{X}}}-{M}.{E}.={172.3}\)
(2) \(\displaystyle\overline{{{X}}}+{M}.{E}.={229.1}\)
By adding (1) and (2), we have
\(\displaystyle{2}\overline{{{X}}}={172.3}+{229.1}\)
\(\displaystyle\overline{{{X}}}={\frac{{{401.4}}}{{{2}}}}\)
\(\displaystyle\overline{{{X}}}={200.7}\)
and,
\(\displaystyle{M}.{E}.={200.7}-{172.3}\)
\(\displaystyle{M}.{E}.={28.4}\)
Answer \(\displaystyle=\bar{X}\pm M.E.=200.7\pm28.4\)

Have a similar question?
Ask An Expert
7
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...