In 2008, the per capita consumption of soft drinks in Country A was reported to

Question

In 2008, the per capita consumption of soft drinks in Country A was reported to be 18.22 gallons. Assume that the per capita consumption of soft drinks in Country A is approximately normally distributed, with a mean of 18.22 gallons and a standard deviation of 4 gallons. Complete parts (a) through (d) below.

a. What is the probability that someone in Country A consumed more than 11 gallons of soft drinks in 2008?

b. What is the probability that someone in Country A consumed between 5 and 9 gallons of soft drinks in 2008?

c. What is the probability that someone in Country A consumed less than 9 gallons of soft drinks in 2008?

d. 99% of the people in Country A consumed less than how many gallons of soft drinks?

Explanation / Answer

= 18.22, = 4

(a) z = (11 - 18.22)/4 = -1.805

P(x > 11) = P(z > -1.805) = 0.9645

(b) z1 = (5 - 18.22)/4 = -3.305 and z2 = (9 - 18.22)/4 = -2.305

P(5 < x < 9) = P(-3.305 < z < -2.205) = 0.0101

(c) P(x < 9) = P(z < -2.305) = 0.0106

(d) z- score for 99th percentile is z = 2.3263

x = + z * = 18.22 + 2.3263 * 4 = 27.53 gallons

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