Find the indicated probability or percentage for the normally distributed variable.
-The variable $X$ is normally distributed.The mean is $\mu = 22.0$ and the standard deviation is $\sigma = 2.4$. Find $P ( 19.7

Question

Find the indicated probability or percentage for the normally distributed variable.
-The variable $X$ is normally distributed.The mean is $\mu = 22.0$ and the standard deviation is $\sigma = 2.4$. Find $P ( 19.7 < X < 25.3 )$.  
A)$0.7477$
B) $1.0847$
C) $0.4107$
D) $0.3370$

Quizplus · Accepted Answer

To find $P(19.7 < X < 25.3)$, we first convert the X values to Z-scores using the formula $Z = \frac{X - \mu}{\sigma}$. For $X = 19.7$, $Z = \frac{19.7 - 22.0}{2.4} = -0.9583$. For $X = 25.3$, $Z = \frac{25.3 - 22.0}{2.4} = 1.375$. Looking these Z-scores up in a standard normal distribution table or using a calculator, we find the probabilities corresponding to these Z-scores and subtract the smaller from the larger to find the probability of X being between 19.7 and 25.3. The result is approximately 0.7477, indicating that there is a 74.77% chance that X falls between 19.7 and 25.3.

Find the Indicated Probability or Percentage for the Normally Distributed XXX

Find the Indicated Probability or Percentage for the Normally Distributed $X$