x is a normally distributed random variable with a mean of 24 and a standard deviation of 6. The probability that x is less than 11.5 is
A) 0.0186.
B) 0.9814.
C) 0.0076.
D) 0.9924.

Question

Quizplus · Accepted Answer

To find the probability that x is less than 11.5, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. Plugging in the given values: Z = (11.5 - 24) / 6 = -12.5 / 6 = -2.083. Looking up this Z-score in a standard normal distribution table or using a calculator gives a probability of approximately 0.0186.

X Is a Normally Distributed Random Variable with a Mean