D

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

536 viewed last edited 1 year ago Anonymous
0 Andrei had cinnamon-scented jar candle that burned for 30 hours and a berry-scented pillar candle that burned for 88 hours.

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

OPTION B.

The berry-scented pillar candle

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 30 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{30-25}{2.5}=\frac{5}{2.5\ }\ =\ 2

Let x_{2} be the number of hours the berry-scented candle burnt, which is given as 88 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{88-95}{7.5}=-\frac{7}{7.5}\ =\ -0.93

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.