Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in "acid rain." The acidity of liquids is measured by pH on a scale of0

0to14.

14.Distilled water has pH7.0,

7.0,and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below5.0.

5.0.

A sample of105

105rainwater specimens had mean pH5.43;

5.43;standard deviation0.54;

0.54;and fivenumber summary4.33,

4.33,5.05,

5.05,5.44,

5.44,5.79,

5.79,6.81.

6.81.

(a) Compare the mean and median and also the distances of the two quartiles from themedian.

Does it appear that the distribution is quite symmetric?Why?

The third quartile is closer to the median than the first quartile is. This indicates that the third quartile may have been pushed down by a righthand skew in thedistribution.

The mean is almost identical to the median, and the quartiles are similar distances from the median. This suggests that the distribution is reasonablysymmetric.

The mean is a relatively resistant measure, while the median isn't. Therefore, the median gets pulled further away from the direction of a long tail. Since the median is lower than the mean, we conclude that the distribution has a righthandtail.

The median is a relatively resistant measure, while the mean isn't. Therefore, the mean gets pulled further away from the direction of a long tail. Since the mean is lower than the median, we conclude that the distribution has a righthandtail.

(b) If the distribution is really(5.43,0.54),

N(5.43,0.54),what proportion of observations would be less than5.05?

5.05?(Enter your answer rounded to four decimalplaces.)

proportion:

If the distribution is really(5.43,0.54)

N(5.43,0.54), what proportion of observations would be less than5.79?

5.79?(Enter your answer rounded to four decimalplaces.)

proportion:

Do these proportions suggest that the distribution is close to Normal?Why?

Yes, because the quartiles are very close to the quartiles of the Normaldistribution.

No, because the Normal distribution has a lower first quartile and a lower thirdquartile.

No, because the Normal distribution has a higher third quartile and a higher firstquartile.

These proportions do not provide information aboutNormality.