Question

X is a normally distributed random variable with mean 54 and standard deviation 4. What is the probability that X is between 50 and 58?

(A) 0.841
(B) 0.159
(C) 0.683
(D) 0.317

Answer 1

The probability that X is between 50 and 58 is approximately 0.6827.

Step-by-step explanation:

To find the probability that X is between 50 and 58, we need to calculate the z-scores for 50 and 58 using the formula:

z = (x - mean) / standard deviation

Using the given mean of 54 and standard deviation of 4, the z-scores for 50 and 58 are:

z(50) = (50 - 54) / 4 = -1

z(58) = (58 - 54) / 4 = 1

We can then use the standard normal distribution table or a calculator to find the area under the normal curve between these z-scores. The area between -1 and 1 is approximately 0.6827. Therefore, the probability that X is between 50 and 58 is approximately 0.6827, which corresponds to option (C).