Final answer:
The new random variable y = 5x - 5 will have a mean (μy) of 45 and a standard deviation (σy) of 15, calculated via linear transformation from the original variables.
Step-by-step explanation:
When you have a distribution, x, with a mean (μ) of 10 and a standard deviation (σ) of 3, and you define a new random variable y = 5x - 5, you can find the new mean and standard deviation by applying linear transformation rules to the original variables. The mean of y (μy) is calculated by taking the coefficient of x in the equation (which is 5) and multiplying it by the mean of x, then adding the constant (-5). Thus, μy = 5 * 10 - 5 = 45.
The standard deviation of y (σy) is found by taking the absolute value of the coefficient of x in the equation (which is 5) and multiplying it by the standard deviation of x. Therefore, σy = |5| * 3 = 15. Note that the constant does not affect the standard deviation, only the mean.