With reference to Example 10.20, find P (712 < M < 725| x̅ = 692).

Example 10.20

A distributor of soft- drink vending machines feels that in a supermarket one of his machines will sell on the average µ₀ = 738 drinks per week. Of course, the mean will vary somewhat from market to market, and the distributor feels that this variation is measured by the standard deviation σ₀ = 13.4. As far as a machine placed in a particular market is concerned, the number of drinks sold will vary from week to week, and this variation is measured by the standard deviation σ = 42.5. If one of the distributor’s machines put into a new supermarket averaged x̅ = 692 during the first 10 weeks, what is the probability (the distributor’s personal probability) that for this market the value of M is actually between 700 and 720?