Question

The annual per capita consumption of bottled water was 32.7 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed

with a mean of 32..7 and a standard deviation of 12 gallons.

a. What is the probability that someone consumed more than 38 gallons of bottled​ water?

b. What is the probability that someone consumed between 30 and 40 gallons of bottled​ water?

c. What is the probability that someone consumed less than 30 gallons of bottled​ water?

d.97.5​% of people consumed less than how many gallons of bottled​ water?

Answer 1

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Normal distribution params are:
Mean = 32.7
Stdev = 12

We employ the formula Z = (X-Mu)/Stdev to standardize a raw score

a. P(X>38), Standardizing:
= P(Z> ( 38-32.7)/12)
= P(Z>0.4417)
= 0.3294

b. P(30<X<40), Standariding using formula Z = (X-Mu)/Stdev we get:
P( (30-32.7)/12 < Z< (40-32.7)/12)
= P(-0.225   <Z< 0.6083)
= .7285 - .4110
= 0.3175

c. P(X<30), Standardizing
= P(Z<-.225)
= .4110

d. Z for 97.5% is 1.96. We referred to Z-table for this.

Raw score for whih 97.5% of people consumed less is :

Mean + Z*Stdev
= 32.7+1.96*12
= 56.22

Answer: 56.22 gallons