Assume that X has a normal distribution, and find the indicated probability.
-The mean is $\mu = 15.2$ .2 and the standard deviation is $\sigma = 0.9$ Find the probability that X is between 14.3 and 16.1.
A) 0.1587
B) 0.8413
C) 0.3413
D) 0.6826

Question

Quizplus · Accepted Answer

We need to find the probability of X being between 14.3 and 16.1. We can find the z-scores for these values:
z1 = (14.3 - 15.2) / 0.9 = -1
z2 = (16.1 - 15.2) / 0.9 = 1
Using a standard normal distribution table, we can find the area/probability between these z-scores:
P(-1 < Z < 1) = 0.6826
Since X follows a normal distribution with mean 15.2 and standard deviation 0.9, the probability of X being between 14.3 and 16.1 is the same as the probability of a randomly selected value falling between -1 and 1 standard deviations from the mean. Therefore, the answer is D.

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