Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

2.1: Examples for Later

  1. Last updated
  2. Save as PDF
  • Page ID
    19630

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    Example \(\PageIndex{1}\)

    In statistics we often want to compare a computed value to see whether it is less than or greater than 5%. This value is called the p-value. Suppose the calculator gives us that the p-value is 0.0413. Convert this value to a percent and decide how it compares to 5%.

    Solution

    We move the decimal 0.0413 two places to the right to get

    4.13%

    We can now see that 4.13% is less than 5%.

    (not for this section, but keeping for now until I work on the order of operations section)

    Example \(\PageIndex{7}\)

    The "z-score" is defined by:

    \(z=\frac{x-\mu}{\sigma}\)

    Find the z-score rounded to one decimal place if:

    \(x=2.323,\:\mu=1.297,\:\sigma=0.241\)

    Solution

    We can put these numbers into the z-score formula and use a computer or calculator to get

    \(\frac{2.323-1.297}{0.241}\:=\:4.25726141\)

    Now round to one decimal place to get 4.3. Notice that if you rounded before you did the arithmetic, you would get exactly 5 which is very different. 4.3 is more accurate.