Final answer:
The probability that x is less than 6 in a normal distribution with a mean of 5 and a variance of 16 is approximately 0.8413.
Therefore, the answer is c.
Step-by-step explanation:
To calculate the probability that a normally distributed random variable x is less than 6 for a distribution with mean (μ) 5 and variance (σ^2) 16, we first need to know the standard deviation (σ), which is the square root of the variance. Therefore, the standard deviation is 4. We then convert the value x = 6 to a z-score which is (6 - 5) / 4 = 0.25.
The next step is to look up the z-score in a standard normal distribution table or use a statistical software tool to find the cumulative probability for z = 0.25.
The correct cumulative probability associated with z = 0.25 is approximately 0.5987.
To make it relative to our specific distribution, we recall that the probability of being less than the mean (5) is 0.5 in any normal distribution and the probability from the mean (5) to x (6) would add up on it.
However, the value of 0.5987 already accounts for probabilities below the mean since it's for the standard normal distribution.
Therefore, the answer is c) 0.8413, which means that the probability that x is less than 6 is 0.8413.