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 10 gallons.

a. What is the probability that someone consumed more than 33 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. 95​% of people consumed less than how many gallons of bottled​ water?

Answer 1

Solution :

a.

P(x > 33) = 1 - P(x < 33)

= 1 - P[(x - ) / < (33 - 32.7) / 10)

= 1 - P(z < 0.03)

= 1 - 0.512

= 0.488

Probability = 0.0488

b.

P(30 < x < 40) = P[(30 - 32.7)/ 10) < (x - ) /  < (40 - 32.7) / 10) ]

= P(-0.27 < z < 0.73)

= P(z < 0.73) - P(z < -0.27)

= 0.7673 - 0.3936

= 0.3737

Probability = 0.3737

c.

P(x < 30) = P[(x - ) / < (30 - 32.7) / 10]

= P(z < -0.27)

= 0.3936

Probability = 0.3936

d.

Using standard normal table,

P(Z < z) = 95%

P(Z < 1.65) = 0.95

z = 1.65

Using z-score formula,

x = z * +

x = 1.65 * 10 + 32.7 = 49.2

49.2 gallons of bottled​ water