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Some More Normal Curve Problems
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7.8
Find the area under the standard normal curve which lies
(a)
between z = -0.78 and z = 0;
(c) to the left of z = - 155
(b)
to the left of z = 2.50;
(d) between z = 0.33 and z = 0.66
7.9
(a)
(b)
(c)
(d)
Find the area under the standard normal curve which lies
between z = 0 and z = 0.95;
to the right of z = -0.75;
to the right of z = 1.66;
between z = -1.12 and z = - 1.08.
7.10
(a)
(b)
(c)
(d)
Find the area under the standard normal curve which lies
between z = -0.25 and z = 0.25;
between z = -1.88 and z = 1.09;
between z = 2.16 and z = 2.54;
between z = -2.05 and z = -1.24.
7.11
(a)
(b)
(c)
(d)
Find z if
the normal-curve area between 0 and z is 0.3340;
the normal-curve area to the left of z is 0.6517;
the normal-curve area to the left of z is 0.3085;
the normal-curve area between - z and z is 0.9700.
7.12
(a)
(b)
(c)
(d)
Find z if
the normal-curve area between 0 and z is 0.2019;
the normal-curve area to the right of z is 0.8810;
the normal-curve area to the right of z is 0.0336;
the normal-curve area between -z and z is 0.2662.
7.13
(a)
(b)
(c)
(d)
Find z if
the normal-curve area between 0 and -z is 0.4573;
the normal-curve area to the left of z is 0.0838;
the normal-curve area to the left of: is 0.9713;
the normal-curve area between -z and z is 0.5878.
7.14
A random variable has a normal distribution with  = 75.0 and  = 4.8. What are the probabilities that this random variable
will take on a value
(a)
less than 82.2;
(c) between 75.0 and 76.2;
(b)
greater than 71.4;
(d) between 66.6 and 83.4?
7.15
A random variable has a normal distribution with  = 54.2 and  = 4.4. What are the probabilities that this random variable
will take on a value
(a)
less than 63.0:
(c) between 43.2 and 65.2;
(b)
less than 46.5;
(d) between 48.7 and 64.1?
7.16
(a)
(b)
(c)
(d)
Find the probabilities that a random variable having a normal distribution will take on a value within
one standard deviation of the mean;
two standard deviations of the mean;
three standard deviations of the mean;
four standard deviations of the mean.
Some More Normal Curve Problems
7.18
A normal distribution has the mean  = 61.6. Find its standard deviation if 20% of the total area under the curve lies to the
right of 70.0.
7.19
A normal distribution has the mean  = 74.4. Find its standard deviation if 10% of the area under the curve lies to the right
of 100.0.
7.20
A random variable has a normal distribution with the standard deviation  = 10. Find its mean if the probability is 0.8264
that it will take on a value less than 77.5.
7.21
For a certain random variable having the normal distribution, the probability is 0.33 that it will take on a value less than
245, and the probability is 0.48 that it will take on a value greater than 260. Find the mean and the standard deviation of this random
variable.
7.22
In an experiment to determine the amount of time required to assemble an easy to assemble” toy, the assembly time was
found to be a random variable having approximately a normal distribution with  = 27.8 minutes and  = 4.0 minutes. What are the
probabilities that this kind of toy can be assembled in
(a)
less than 25.0 minutes;
(b)
anywhere from 26.0 to 29.6 minutes?
7.23
A salesman who frequently drives from Boston to New York finds that his driving time is a random variable having
roughly a normal distribution with  = 4.3 hours and  = 0.2 hour. Find the probabilities that such a trip will take
(a)
more than 4.5 hours;
(b)
less than 4.0 hours.
7.24
With reference to the preceding exercise, below what value (number of hours) are the fastest 25% of his trips?
7.25
Suppose that during periods of relaxation therapy the reduction of a person’s oxygen consumption may be looked upon as
a random variable having a normal distribution with  = 38.6 cubic centimeters (cc) per minute and  = 4.3 cc per minute. Find the
probabilities that during a period of relaxation therapy a person’s oxygen consumption will be reduced by
(a)
at least 40.0 cc per minute;
(b)
anywhere from 35.0 to 45.0 cc per minute.
7.26
The lengths of the sardines received by a cannery have a mean  = 4.64 inches and a standard deviation  = 0.25 inch. If
the distribution of these lengths can be approximated closely with a normal distribution, what percentage of all these sardines are
(a)
shorter than 4.00 inches;
(b)
from 4.40 to 4.80 inches long?
7.27
With reference to the preceding exercise, above which length lies the longest 10% of the sardines?
Some More Normal Curve Problems
Some Answers
7.8
7.9
7.10
7.12
7.13
7.14
7.15
7.16
7.19
7.20
7.21
7.23
7.24
7.25
7.26
7.27
(a) 0.2823; (b) 0.9938; (c) 0.0606; (d) 0.1161.
(a) 0.3289; (b) 0.7734; (c) 0.0485; (d) 0.0087.
(a) 0.1974; (b) 0.8320; (c) 0.0099; (d) 0.0873.
(a) z = 0.53 or z = -0.53; (b)-1.18; (c) 1.83; (d) z = 0.34 or z = -0.34.
(a) z = 1.72 or z = -1.72; (b) -1.38; (c) 1.90; (d) z = 0.82 or z = -0.82.
(a) 0.9332; (b) 0.7734; (c) 0.0987; (d) 0.9198.
(a) 0.9772; (b) 0.0401; (c) 0.9876; (d) 0.8822.
(a) 0.6826; (b) 0.9544; (c) 0.9974; (d) 0.99994.
20.
68.1.
 = 258.47;  = 30.61.
(a) 0.1587; (b) 0.0668.
4.17 hours.
(a) 0.3707; (b) 0.7314.
(a) 0.52% (b) 57.04%