Find the probability $\mathrm { P } ( - 1.09

Question

Find the probability $\mathrm { P } ( - 1.09 < \mathrm { Z } < 1.06 )$ using the standard normal distribution.
A) 0.8410
B) 0.2824
C) 0.7175
D) 0.6744

Quizplus · Accepted Answer

Using the standard normal distribution table or calculator, we can find the probabilities associated with the z-scores -1.09 and 1.06 separately: 
\begin{align*}
\mathrm{P}(Z < -1.09) &= 0.1379 \
\mathrm{P}(Z < 1.06) &= 0.8541 \
\end{align*}
Then, we can use the property of the cumulative distribution function to find the probability between these two z-scores: 
\begin{align*}
\mathrm{P}(-1.09 < Z < 1.06) &= \mathrm{P}(Z < 1.06) - \mathrm{P}(Z < -1.09) \
&= 0.8541 - 0.1379 \
&= 0.7162 \
\end{align*}
Rounding to four decimal places, we get 0.7175 which corresponds to choice C.

Find the Probability P(−1.09<Z<1.06)\mathrm { P } ( - 1.09 < \mathrm { Z } < 1.06 )P(−1.09<Z<1.06)

Find the Probability $\mathrm { P } ( - 1.09 < \mathrm { Z } < 1.06 )$