Inverse normal (kevin)

[Stevensmay]

Question asked over IRC. Solved.

Zhoe finds a more efficient way of performing the task. the time taken, using the new method, is also a normally distributed random  variable with mean of 100. If 20% of the time the task takes more than two hours to complete. What is the standard deviation of random variable?

First we recognize what we have, and what we want to find. We know the mean is 100, and also have an x-value and area. We want to find the standard deviation.

First we find the z score that covers 80% of the area under the curve, giving us a number for how many tasks will be completed in under 2 hours. The area past this z score will be 20%.
Using CAS, Inverse normal with area of .8, mean 0 and s.d 1.

We now have a z score for 20% of the tasks in terms of time.
Put this into the z score conversion formula which is

We get

Rearranging for this gives us a standard deviation of 24 minutes (rounded.

[Stevensmay]

Question was posed over IRC, easier to answer here. Thought I included that in the original post, thank you.

[kevinnguyen]

thanks

[Stevensmay]

The probability the chef orders large sized eggs today and medium sized eggs tomorrow is 0.55. What is probability that chef orders medium sized today and large tomorrow.



Matrix labelled such that

In order to find the probability from a transition matrix, we first find the event along the top that we want (today) , followed by the event down the side (tomorrow).
So for medium today, we find medium along the top row, large tomorrow is large on the vertical row. We come to the cell containing a value of .75, which is our probability.