Question

The annual per capita consumption of bottled water was 32.232.2 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 32.232.2 and a standard deviation of 1313

gallons.

a. What is the probability that someone consumed more than 3737 gallons of bottled​ water?

b. What is the probability that someone consumed between 2525 and 3535 gallons of bottled​ water?

c. What is the probability that someone consumed less than 2525 gallons of bottled​ water?

d. 9999​% of people consumed less than how many gallons of bottled​ water?

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	32.2
std deviation   =σ=	13

probability =

P(X>37)

=

P(Z>0.37)=

1-P(Z<0.37)=

1-0.6443=

0.3557

b)

probability =

P(25<X<35)

=

P(-0.55<Z<0.22)=

0.5871-0.2912=

0.2959

c)

probability =

P(X<25)

=

P(Z<-0.55)=

0.2912

d)

for 99th percentile critical value of z=		2.33
therefore corresponding value=mean+z*std deviation=			62.49 gallon