Given that X is a normally distributed random variable with a mean of 52 and a standard deviation of 2,the probability that X is between 48 and 56 is:
A)0.0896
B)0.4104
C)0.5896
D)0.9544

Question

Quizplus · Accepted Answer

To solve this problem, we need to standardize X to a standard normal distribution using the formula z = (X-μ)/σ, where μ = 52 and σ = 2.

For X = 48, z = (48 - 52)/2 = -2. 
For X = 56, z = (56 - 52)/2 = 2.

Using a standard normal distribution table, we can find the probability of being between -2 and 2, which is 0.9544. Therefore, the answer is D.

Given That X Is a Normally Distributed Random Variable with a Mean