For 261 female heights, the mean was 64.6 inches and the standard deviation was 2.6 inches. The shortest person in this sample had a height of 55 inches.

(a) Find the z-score for the height of 55 inches. z = ______________ (3 decimal places) (b) What does the (positive or negative) sign for the z-score represent?

The height is above the mean.

The height is below the mean.

The height is a potential outlier.

The height is not a potential outlier.

(c) Assuming the distribution of heights is approximately bell-shaped, is this observation a potential outlier according to the three standard deviation distance criterion? Explain.

Yes, it is less than 3 standard deviations away from the mean.

Yes, it is more than 3 standard deviations away from the mean.

No, it is less than 3 standard deviations away from the mean.

No, it is more than 3 standard deviations away from the mean.