Alkalinityofriverwater. Thealkalinitylevelofwaterspec- imens collected from the

Question

Alkalinityofriverwater.Thealkalinitylevelofwaterspec- imens collected from the Han River in Seoul, Korea, has a mean of 50 milligrams per liter and a standard deviation of 3.2 milligrams per liter. (Environmental Science & Engineering, Sept. 1, 2000.) Assume the distribution of alkalinity levels is approximately normal and find the probability that a water specimen collected from the river has an alkalinity level

a. exceeding 45 milligrams per liter.
b. below 55 milligrams per liter.
c. between51and52milligramsperliter.

Explanation / Answer

SolutionA:

mean=50

stddev=3.2

P(X>45)

z=x-mean/sd

=45-50/3.2

=-5/3.2

= -1.5625

P(Z>-1.5625)

1-pnorm( -1.5625)

0.9409149

ANSWER:0.9409149

sOLUTIONB:

P(X<55)

z=55-50/3.2

=5/3.2

=1.5625

P(Z<1.5625)

pnomr(1.5625)

= 0.9409149

ANSWER:0.9409

Solutionc:

P(51<x<52)

P(51-50/3.2<Z<52-50/3.2)

=P(0.3125<Z<0.625)

=P(Z<0.625)-P(Z<0.3125)

=pnorm(0.625)-pnorm(0.3125)

=0.1113

ANSWER:0.1113

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