Question

In: Statistics and Probability

Let X = tool life (measured in some unit of time) of the current tool type....

  1. Let X = tool life (measured in some unit of time) of the current tool type. Let Y = tool life of the new tool type being considered. The standard deviations of X and Y are both equal to 2. Through tests the mean tool life of Y was shown to be statistically significantly greater than X at a significance level of 0.05. The mean of X is estimated to be 10, and the mean of Y is estimated to be 10.5. Assume that both X and Y are normally distributed.
    1. What is the probability that a randomly observed value of tool life X is greater than Y? (hint: the variance of the difference of two random variables is sum of their variances, and the difference of two independent normal random variables is normally distributed).
    2. How much greater would the mean of Y have to be so that the chance that a randomly observed value of tool life X is greater than Y is less than 0.05?

Solutions

Expert Solution

I answer the above questions using the basic knowledge of standard normal variable and their differences,

and the distribution of their differences.

The answers are given in subparts as given in the question.

orchestra answered 1 year ago
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