3301 Statistics

Question

The burning times of scented candles, in minutes, are normally distributed with a mean of 249 and a standard deviation of 20. Find the number of minutes a scented candle burns if it burns for a shorter time than 80% of all scented candles.

Answer 1

If it burns for a shorter time than 80% of the scented candles, it is the 20th percentile. First we need to find the z-score for the 20% percentile which is approximately -0.84.

z = (x - mean)/ standard deviation, so

-0.84 = (x - 249)/20

x = 20(-0.84)+249 = 232.2