Page 149 - Applied statistics and probability for engineers

Section 4-6/Normal Distribution 127

(b) What is the probability that a line width is between 0.47 (b) What thickness is exceeded by 95% of the samples?
and 0.63 micrometer? (c) If the speciications require that the thickness is between
(c) The line width of 90% of samples is below what value? 1.39 cm and 1.43 cm, what proportion of the samples meets
4-76. The ill volume of an automated illing machine used speciications?
for illing cans of carbonated beverage is normally distributed 4-82. The demand for water use in Phoenix
with a mean of 12.4 luid ounces and a standard deviation of 0.1 in 2003 hit a high of about 442 million gallons per day on June
luid ounce. 27 (http://phoenix.gov/WATER/wtrfacts.html). Water use in the
(a) What is the probability that a ill volume is less than 12 summer is normally distributed with a mean of 310 million gal-
luid ounces? lons per day and a standard deviation of 45 million gallons per
day. City reservoirs have a combined storage capacity of nearly
(b) If all cans less than 12.1 or more than 12.6 ounces are
350 million gallons.
scrapped, what proportion of cans is scrapped?
(c) Determine speciications that are symmetric about the (a) What is the probability that a day requires more water than
mean that include 99% of all cans. is stored in city reservoirs?
(b) What reservoir capacity is needed so that the probability
4-77. In the previous exercise, suppose that the mean of the
illing operation can be adjusted easily, but the standard devia- that it is exceeded is 1%?
tion remains at 0.1 luid ounce. (c) What amount of water use is exceeded with 95% probability?
(d) Water is provided to approximately 1.4 million people.
(a) At what value should the mean be set so that 99.9% of all
What is the mean daily consumption per person at which
cans exceed 12 luid ounces?
the probability that the demand exceeds the current reser-
(b) At what value should the mean be set so that 99.9% of all
cans exceed 12 luid ounces if the standard deviation can be voir capacity is 1%? Assume that the standard deviation of
reduced to 0.05 luid ounce? demand remains the same.
4-83. The life of a semiconductor laser at a constant power is
4-78. A driver’s reaction time to visual stimulus is nor-
mally distributed with a mean of 0.4 seconds and a standard normally distributed with a mean of 7000 hours and a standard
deviation of 0.05 seconds. deviation of 600 hours.
(a) What is the probability that a laser fails before 5000 hours?
(a) What is the probability that a reaction requires more than
(b) What is the life in hours that 95% of the lasers exceed?
0.5 seconds?
(c) If three lasers are used in a product and they are assumed to
(b) What is the probability that a reaction requires between 0.4 fail independently, what is the probability that all three are
and 0.5 seconds?
still operating after 7000 hours?
(c) What reaction time is exceeded 90% of the time?
4-84. The diameter of the dot produced by a printer is nor-
4-79. The speed of a ile transfer from a server on campus to a
mally distributed with a mean diameter of 0.002 inch and a
personal computer at a student’s home on a weekday evening is
standard deviation of 0.0004 inch.
normally distributed with a mean of 60 kilobits per second and
(a) What is the probability that the diameter of a dot exceeds
a standard deviation of four kilobits per second.
0.0026?
(a) What is the probability that the ile will transfer at a speed
of 70 kilobits per second or more? (b) What is the probability that a diameter is between 0.0014
and 0.0026?
(b) What is the probability that the ile will transfer at a speed
(c) What standard deviation of diameters is needed so that the
of less than 58 kilobits per second?
probability in part (b) is 0.995?
(c) If the ile is one megabyte, what is the average time it will
take to transfer the ile? (Assume eight bits per byte.) 4-85. The weight of a sophisticated running shoe is normally
4-80. In 2002, the average height of a woman aged 20–74 years distributed with a mean of 12 ounces and a standard deviation
was 64 inches with an increase of approximately 1 inch from 1960 of 0.5 ounce.
(http://usgovinfo.about.com/od/healthcare). Suppose the height (a) What is the probability that a shoe weighs more than
of a woman is normally distributed with a standard deviation of 13 ounces?
two inches. (b) What must the standard deviation of weight be in order for
(a) What is the probability that a randomly selected woman in the company to state that 99.9% of its shoes weighs less
this population is between 58 inches and 70 inches? than 13 ounces?
(b) What are the quartiles of this distribution? (c) If the standard deviation remains at 0.5 ounce, what must
(c) Determine the height that is symmetric about the mean that the mean weight be for the company to state that 99.9% of
includes 90% of this population. its shoes weighs less than 13 ounces?
(d) What is the probability that ive women selected at random 4-86. Measurement error that is normally distributed with a
from this population all exceed 68 inches? mean of 0 and a standard deviation of 0.5 gram is added to the
4-81. In an accelerator center, an experiment needs a 1.41-cm- true weight of a sample. Then the measurement is rounded to
thick aluminum cylinder (http://puhep1.princeton.edu/mumu/ the nearest gram. Suppose that the true weight of a sample is
target/Solenoid_Coil.pdf). Suppose that the thickness of a cyl- 165.5 grams.
inder has a normal distribution with a mean of 1.41 cm and a (a) What is the probability that the rounded result is 167 grams?
standard deviation of 0.01 cm. (b) What is the probability that the rounded result is 167 grams
(a) What is the probability that a thickness is greater than 1.42 cm? or more?