Find $\mathrm { P } ( \bar { X }

Question

Find $\mathrm { P } ( \bar { X } < 402 )$ If ? = 400,?_x = 200,and n = 100. A).8413 B).4602 C).5398 D).1587

Quizplus · Accepted Answer

First we need to find the z-score for 402:

\begin{align*}
z &= \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}} \
&= \frac{402 - 400}{\frac{200}{\sqrt{100}}} \
&= \frac{2}{20} \
&= 0.1
\end{align*}

Then we need to find the area to the left of this z-score using a standard normal distribution table, or a calculator:

\begin{align*}
P(\bar{X} < 402) &= P(z < 0.1) \
&\approx 0.5398
\end{align*}

Therefore, the best choice is C, with a probability of 0.5398.

Find P(Xˉ<402)\mathrm { P } ( \bar { X } < 402 )P(Xˉ<402)

Find $\mathrm { P } ( \bar { X } < 402 )$