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 60% of all scented candles.

The candle burns for 244 minutes.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

Find the number of minutes a scented candle burns if it burns for a shorter time than 60% of all scented candles.

This is the 100-60 = 40th percentile, which is X when Z has a pvalue of 0.4. So X when Z = -0.253.

The candle burns for 244 minutes.

60

step-by-step explanation: