Assume that X has a normal distribution, and find the indicated probability.
-The mean is $\mu = 22.0$ .0 and the standard deviation is $\sigma = 2.4$ Find the probability that X is between 19.7 and 25.3.
A) 0.3370
B) 0.7477
C) 1.0847
D) 0.4107

Question

Quizplus · Accepted Answer

Using the standard normal distribution, we can convert the values of X into z-scores:
z1 = (19.7 - 22.0) / 2.4 = -0.9583
z2 = (25.3 - 22.0) / 2.4 = 1.375
Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:
P(-0.9583 < Z < 1.375) = 0.7477
Therefore, the probability that X is between 19.7 and 25.3 is 0.7477.

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