D

#### Here are some summary statistics for the durations for which candles from a certain company burn.

7 viewed last edited 6 months ago Anonymous
0 Andrei had cinnamon-scented jar candle that burned for 40 hours and a berry-scented pillar candle that burned for 98 hours.

Relative to its type, which candle burned faster? Sahil Khan
0

Recall what a z-score is

The formula for calculating the z-score is \frac{x- \mu}{\sigma}

Let x_{1} be the number of hours the cinnamon-scented jar candle burnt, which is given as 40 hours. The mean and standard deviation are \mu_{1}= 25, and \sigma_{1}= 2.5

The z-score for the 1st candle,

z_{1} = \frac{x_{1} - \mu_{1}}{\sigma_{1}},

z_{1} = \frac{40 - 25}{2.5} = 6

Let x_{2} be the number of hours the berry-scented candle burnt, which is given as 98 hours.

The mean and the standard deviation are \mu_{2} = 95 and \sigma_{2}= 7.5

The z-score for the 2nd candle,

z_{2} = \frac{x_{2} - \mu_{2}}{\sigma_{2}},

z_{2} = \frac{98 - 95}{7.5} = 0.4

The berry-scented candle had the lower z-score, so its duration was farther below average.

So, the berry-scented pillar candle burned faster relative to its type.