Microwave Oven

[deepak.yadav]

In a certain microwave oven on high power, the time it takes a randomly chosen kernel of popcorn to pop is normally distributed with a mean of 140 seconds and a standard deviation of 25 seconds. What percentage of kernels will fail to pop if the popcorn is cooked for
(a) 2 minutes? (b) 3 minutes? (c) if you wanted 95% of the kernels to pop, what time would you allow? (d) If you wanted 99% to pop?

[dundurn]

You can use the NORMDIST function in Excel to plug in the values you have and extract those you require.

Approximately 68% of grains will pop within 1SD either side of the mean. This means around 16% will pop below the 115s value and another 16% will fail to pop unless you cook them for more than 165s. Similarly approx 95% pop within 2SD of the mean and 99% within 3SD. You can use these facts to second guess the values you calculate.

Using NORMDIST with a value of 120s gives 21.2% popped, so 78.8% unpopped.
A value of 180s gives 94.5% so 4.5% unpopped.

A bit of trial and error inserting different time values (I'm sure I could have used a goal-seek formula, but it is 2 in the morning!) gives 181.2s to produce 95% popped and 198.2s to give 99%.

I imagine if you're actually doing a stats course you have formulae which would produce similar values if you bothered to use them?