Question

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 of 00 to 14.14. Distilled water has pH 7.0,7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below 5.0.5.0.

A sample of 105105 rainwater specimens had mean pH 5.43;5.43; standard deviation 0.54;0.54; and five‑number summary 4.33,4.33, 5.05,5.05, 5.44,5.44, 5.79,5.79, 6.81.6.81.

(b) If the distribution is really ?(5.43,0.54),N(5.43,0.54), what proportion of observations would be less than 5.05?5.05? (Enter your answer rounded to four decimal places.)

proportion:

(c)If the distribution is really ?(5.43,0.54)N(5.43,0.54), what proportion of observations would be less than 5.79?5.79? (Enter your answer rounded to four decimal places.)

proportion:

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

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

b. These proportions do not provide information about Normality.

c. Yes, because the quartiles are very close to the quartiles of the Normal distribution.

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

Answer 1

ANSWER::

Given that, X ~ N(5.43, 0.54)

Mean = 5.43 and

Standard deviation = 0.54

b) We want to find, P(X < 5.05)

Therefore, required probability is 0.2420

c) We want to find, P(X < 5.79)

Therefore, required probability is 0.7486

Therefore, required probability is :: 74.86

Option :: (c) is correct.........

Ans:: Yes, because the quartiles are very close to the quartiles of the Normal distribution.

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