Question

The annual per capita consumption of bottled water was 33.3 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 33.3 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 20 and 30 gallons of bottled​ water?

c. What is the probability that someone consumed less than 20 gallons of bottled​ water?

d. 90​% of people consumed less than how many gallons of bottled​ water?

Answer 1

µ = 33.3, σ = 12

a) Probability that someone consumed more than 38 gallons of bottled​ water, P(X > 38) =

= P( (X-µ)/σ > (38-33.3)/12)

= P(z > 0.3917)

= 1 - P(z < 0.3917)

Using excel function:

= 1 - NORM.S.DIST(0.3917, 1)

= 0.3477

b) Probability that someone consumed between 20 and 30 gallons of bottled​ water, P(20 < X < 30) =

= P( (20-33.3)/12 < (X-µ)/σ < (30-33.3)/12 )

= P(-1.1083 < z < -0.275)

= P(z < -0.275) - P(z < -1.1083)

Using excel function:

= NORM.S.DIST(-0.275, 1) - NORM.S.DIST(-1.1083, 1)

= 0.2578

c) Probability that someone consumed less than 20 gallons of bottled​ water, P(X < 20) =

= P( (X-µ)/σ < (20-33.3)/12 )

= P(z < -1.1083)

Using excel function:

= NORM.S.DIST(-1.1083, 1)

= 0.1339

d) P(x < a) = 0.9

Z score at p = 0.9 using excel = NORM.S.INV(0.9) =1.2816

Value of X = µ + z*σ = 33.3 + (1.2816)*12 = 48.68 gallons