Statpro Practice question and Answer Verified
DONE An employee is selected from a staff of 10 to super-vise a certain project by
selecting a tag at random from a box containing 10 tags numbered from 1 to 10.
Find the formula for the probability distribution of X rep-resenting the number on
the tag that is drawn. What is the probability that the number drawn is less than
4? - ✔✔3/10
According to Chemical Engineering Progress (November 1990), approximately 30%
of all pipework failures in chemical plants are caused by operator error.
(a) What is the probability that out of the next 20 pipework failures at least 10 are
due to operator error?
(b) What is the probability that no more than 4 out of 20 such failures are due to
operator error?
(c) Suppose, for a particular plant, that out of the ran-dom sample of 20 such
failures, exactly 5 are due to operator error. Do you feel that the 30% figure stated
above applies to this plant? Comment. - ✔✔(a) 0.0480; (b) 0.2375; (c) P (X =5 | p
=0.3) =0.1789, P =0.3 is reasonable.
DONE One prominent physician claims that 70% of those with lung cancer are
chain smokers. If his assertion is correct,
(a) find the probability that of 10 such patientsrecently admitted to a hospital,
fewer than half are chain smokers;
(b) find the probability that of 20 such patients re-cently admitted to a hospital,
fewer than half are chain smokers. - ✔✔(a) 0.0474; (b) 0.0171
DONE In testing a certain kind of truck tire over rugged terrain, it is found that
25% of the trucks fail to com-plete the test run without a blowout. Of the next 15
trucks tested, find the probability that
, (a) from 3 to 6 have blowouts;
(b) fewer than 4 have blowouts;
(c) more than 5 have blowouts. - ✔✔(a) 0.7073; (b) 0.4613; (c) 0.1484
DONE The probability that a patient recovers from a delicate heart operation is
0.9. What is the probabil-ity that exactly 5 of the next 7 patients having this
operation survive? - ✔✔0.1240
DONE A national study that examined attitudes about antidepressants revealed
that approximately 70% of re-spondents believe "antidepressants do not really
cure anything, they just cover up the real trouble." Accord-ing to this study, what
is the probability that at least 3 of the next 5 people selected at random will hold
this opinion? - ✔✔0.8369
DONE It is known that 60% of mice inoculated with a serum are protected from a
certain disease. If 5 mice are inoculated, find the probability that
(a) none contracts the disease;
(b) fewer than 2 contract the disease;
(c) more than 3 contract the disease. - ✔✔(a) 0.0778; (b) 0.3370; (c) 0.0870
If X represents the number of people in Exer-cise 5.13 who believe that
antidepressants do not cure but only cover up the real problem, find the mean
and variance of X when 5 people are selected at random. - ✔✔μ =3.5, σ2 =1.05
The surface of a circular dart board has a small center circle called the bull's-eye
and 20 pie-shaped re-gions numbered from 1 to 20. Each of the pie-shaped
regions is further divided into three parts such that a person throwing a dart that
lands in a specific region scores the value of the number, double the number, or
DONE An employee is selected from a staff of 10 to super-vise a certain project by
selecting a tag at random from a box containing 10 tags numbered from 1 to 10.
Find the formula for the probability distribution of X rep-resenting the number on
the tag that is drawn. What is the probability that the number drawn is less than
4? - ✔✔3/10
According to Chemical Engineering Progress (November 1990), approximately 30%
of all pipework failures in chemical plants are caused by operator error.
(a) What is the probability that out of the next 20 pipework failures at least 10 are
due to operator error?
(b) What is the probability that no more than 4 out of 20 such failures are due to
operator error?
(c) Suppose, for a particular plant, that out of the ran-dom sample of 20 such
failures, exactly 5 are due to operator error. Do you feel that the 30% figure stated
above applies to this plant? Comment. - ✔✔(a) 0.0480; (b) 0.2375; (c) P (X =5 | p
=0.3) =0.1789, P =0.3 is reasonable.
DONE One prominent physician claims that 70% of those with lung cancer are
chain smokers. If his assertion is correct,
(a) find the probability that of 10 such patientsrecently admitted to a hospital,
fewer than half are chain smokers;
(b) find the probability that of 20 such patients re-cently admitted to a hospital,
fewer than half are chain smokers. - ✔✔(a) 0.0474; (b) 0.0171
DONE In testing a certain kind of truck tire over rugged terrain, it is found that
25% of the trucks fail to com-plete the test run without a blowout. Of the next 15
trucks tested, find the probability that
, (a) from 3 to 6 have blowouts;
(b) fewer than 4 have blowouts;
(c) more than 5 have blowouts. - ✔✔(a) 0.7073; (b) 0.4613; (c) 0.1484
DONE The probability that a patient recovers from a delicate heart operation is
0.9. What is the probabil-ity that exactly 5 of the next 7 patients having this
operation survive? - ✔✔0.1240
DONE A national study that examined attitudes about antidepressants revealed
that approximately 70% of re-spondents believe "antidepressants do not really
cure anything, they just cover up the real trouble." Accord-ing to this study, what
is the probability that at least 3 of the next 5 people selected at random will hold
this opinion? - ✔✔0.8369
DONE It is known that 60% of mice inoculated with a serum are protected from a
certain disease. If 5 mice are inoculated, find the probability that
(a) none contracts the disease;
(b) fewer than 2 contract the disease;
(c) more than 3 contract the disease. - ✔✔(a) 0.0778; (b) 0.3370; (c) 0.0870
If X represents the number of people in Exer-cise 5.13 who believe that
antidepressants do not cure but only cover up the real problem, find the mean
and variance of X when 5 people are selected at random. - ✔✔μ =3.5, σ2 =1.05
The surface of a circular dart board has a small center circle called the bull's-eye
and 20 pie-shaped re-gions numbered from 1 to 20. Each of the pie-shaped
regions is further divided into three parts such that a person throwing a dart that
lands in a specific region scores the value of the number, double the number, or
