Dr Pepper is a carbonated soft drink marketed as having a unique flavor. The dri

Question

Dr Pepper is a carbonated soft drink marketed as having a unique flavor. The drink was created in the 1880s by Charles Alderton in Waco, Texas and first served around 1885. Dr Pepper was first nationally marketed in the United States in 1904 and is now also sold in Europe, Asia, Canada, Mexico, Australia, New Zealand (as an imported drink), South Africa (also as an imported drink), and South America. Variants include a version without high fructose corn syrup, Diet Dr Pepper, as well as a line of additional flavors, first introduced in the 2000s. W.W Clements, former CEO and president of the Dr Pepper/7-Up Company, described the taste of Dr Pepper as one-of-a-kind, saying, "I've always maintained you cannot tell anyone what Dr Pepper tastes like because it's so different. It's not an apple, it's not an orange, it's not a strawberry, it's not a root beer, it's not even a cola. It's a different kind of drink with a unique taste all its own." The company currently has headquarters in Plano, Texas, and the Dr. Pepper Museum is located in Waco, Texas. [source: Wikipedia]. Of interest is the quantity of Dr Pepper, measured in ounces, that a person consumes when they drink Dr Pepper served from a fountain machine. Suppose that the quantity of Dr Pepper consumed follows an approximate normal distribution with mean 34 ounces and standard deviation 5.8 ounces. Use this information to answer questions 3 and 4. Please circle your final answers. 4. (A) Shevani does not like soft drinks, and hence consumes very little Dr Pepper. Based on the distribution described above, how many ounces of Dr Pepper would a person need to consume to fall in the bottom 4.01% of the distribution? (6 pts) Suppose the ages of employees at the Dr Pepper Snapple Bottling Company follow an approximate normal distribution with a mean of 42.2 years and a standard deviation of 7.8 years. Use this information to answer 4.(B). Please circle your final answer. (B) Chnar and Rommy both work for the Dr Pepper Snapple Bottling Company; Chnar is 30 years old, while Rommy is 51 years old. Based on the distribution described above, what is the probability that the age of an employee will be between 30 and 51 years old? (7 pts)

Explanation / Answer

Answer:

4A.

Z value for bottom 4.01% is -1.75

X= mean+z*sd

=34 -1.75*5.8

=23.85

4B.

Z value for 30, z =(30-42.2)/7.8 = -1.56

Z value for 51, z =(51-42.2)/7.8 = 1.13

P( 30<x<51) = P( -1.56<z<1.13)

= P( z < 1.13) – P( z < -1.56)

=0.8708 - 0.0594

=0.8114

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