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Natasha records the price for a gallon of home-heating oil from 10 randomly selected providers in her region on May 15. She does it again with another 10 randomly selected providers on November 15. The results (in dollars) are shown in the accompanying samples. Calculate the z-score of the data value $2.899 for each of the two dates using a TI-83 or TI-84 graphing calculator.

Round the z-scores to two decimal places. Do not round until you've calculated your final answer

May 15 November 15
2.799 2.959
2.739 3.039
2.699 2.969
2.759 3.059
2.689 2.999
2.749 2.919
2.719 3.149
2.799 2.999
2.819 3.089
2.779 2.989

Respuesta :

To calculate the z-score for the data value $2.899 on May 15, we can use the formula:

z = (x - μ) / σ

where x is the data value, μ is the mean, and σ is the standard deviation.

First, let's calculate the mean and standard deviation for the May 15 data:

Mean (μ) = (2.799 + 2.739 + 2.699 + 2.759 + 2.689 + 2.749 + 2.719 + 2.799 + 2.819 + 2.779) / 10 = 2.761

Standard Deviation (σ) = √[((2.799-2.761)² + (2.739-2.761)² + ... + (2.779-2.761)²) / 10] ≈ 0.033

Now, let's calculate the z-score for $2.899 on May 15:

z = (2.899 - 2.761) / 0.033 ≈ 4.18

Rounding the z-score to two decimal places, the z-score for $2.899 on May 15 is approximately 4.18.

You can follow the same steps to calculate the z-score for November 15 using the provided data.

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