Final answer:
The variance of 2X - 111 is 16/3. The standard deviation of X is 16. The probability P(Y ≤ 60) is approximately 0.8413.
Step-by-step explanation:
For the first question, if X is uniformly distributed between 0 and 4, the variance of 2X - 111 can be found by applying the properties of variance. The variance of a constant times a random variable is equal to the constant squared times the variance of the random variable. In this case, the constant is 2 and the variance of X is (4 - 0)^2/12 = 4/3. So the variance of 2X - 111 would be 2^2 * 4/3 = 16/3.
For the second question, if X is normally distributed with a mean of 3 and a standard deviation of 16, the standard deviation can be found by simply using the given value of the standard deviation, which is 16.
For the third question, to find P(Y ≤ 60) for a normally distributed random variable Y with a mean of 50 and a standard deviation of 10, we can use the Z-score formula. The Z-score is calculated as (60 - 50) / 10 = 1. So we need to find the probability that a Z-score is less than or equal to 1, which is approximately 0.8413.