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ation to the right of the mean.

C. Suppose three randomly selected customers each purchase a

pair of these sneakers. What is the probability that exactly two

of the three buy size 11 sneakers?

6.36 Manufacturing and Product Development Pressurized

carbon dioxide is usually added to soda in order to alleviate the

sweet taste of the drink and to stop some microbes from growing.

While the amount of carbon dioxide varies, most sodas are bottled

under high pressure. The internal pressure of a refrigerated can of

a certain cola has a mean value of 276 kilopascals (kPa) at 16 'C.*

Suppose the pressure is normally distributed, with a standard devi-

ation 7 kPa. A can of this cola (at 16 "C) is randomly selected.

a. What is the probability that the internal pressure is less than

270 kPa?

b. What is the probability that the internal pressure is between 265

and 275 kPa?

C. If the internal pressure is more than 300 kPa when the can is

opened, the liquid will spill out of the can. What is the prob-

ability of a spill?

d. If a person shakes the can for a minimum of 30 seconds, the

mean internal pressure changes to 289 kPa (while the standard

deviation remains the same). What is the probability that the

liquid in a shaken can will spill out when the can is opened?

6.44 Manufacturing and Product Development Classical vin-

lin bows are made from different woods to accommodate musi-

cians' preferences and demands. Some commonly used wood

include snakewood, ironwood, hakia, and pernambuco. While the

bows are carefully handcrafted, they vary slightly in weight

Suppose a bowmaker claims that the weight of his classical bows

3.2 grams,

is normally distributed with mean 60 grams and standard deviation

a. What is the probability that the weight of a randomly selected

ironwood bow is between 58 and 62 grams?

b. Good musicians can detect an unacceptable bow weight (i.e.,

a weight that differs from the mean by more than two standard

coptable?

deviations). What is the probability that a bow weight is unac-

c. Any manufactured bow that weighs more than 66 grams is

reworked in order to decrease the weight. What is the probabil-

ity that a randomly selected ironwood how will need rework?

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