Assume that X has a normal distribution, and find the indicated probability.
-The mean is $\mu = 22.0$ and the standard deviation is $\sigma = 2.4$.
Find the probability that $X$ is between $19.7$ and $25.3$.
A) 1.0847
B) 0.3370
C) 0.4107
D) 0.7477

Question

Assume that X has a normal distribution, and find the indicated probability.
-The mean is $\mu = 22.0$ and the standard deviation is $\sigma = 2.4$.
 Find the probability that $X$ is between $19.7$ and $25.3$.
A) 1.0847
B) 0.3370
C) 0.4107
D) 0.7477

Quizplus · Accepted Answer

To find the probability that $X$ is between $19.7$ and $25.3$, we calculate the z-scores for both values and use the standard normal distribution table. The z-score for $19.7$ is $(19.7 - 22.0) / 2.4 = -0.9583$, and for $25.3$ is $(25.3 - 22.0) / 2.4 = 1.375$. The probability for these z-scores corresponds to approximately 0.7477.

Assume That X Has a Normal Distribution, and Find the Indicated