OWAZ CONTINUOUS DISTRIBUTIONS 145 36. Rock noise in an underground mine occurs at an average rate of three per hour. (See Exercise 65, Chap. 3.) Find the probability that no rock noise will be recorded for at least 30 minutes. 37. California is hit every year by approximately 500 earthquakes that are large enough to be felt. However, those of destructive magnitude occur, on the av- erage, once a year. Find the probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs. (See Exercise 64, Chap. 3.) 38, Consider a chi-squared random variable with 15 degrees of freedom. (a) What is the mean of X?;? What is its variance? (b) What is the expression for the density for X75? (c) What is the expression for the moment generating function for X5? (d) Use Table IV of App. A to find each of the following: 2. P[6.26 < X{s < 27.5] - Xos P[Xis ¥ 5.23] P[X}s²22.3] 2 X95 15 Section 4.4 39. Use Table V of App. A to find each of the following: (a) P[Z< 1.57]. (c) P[Z = 1.57]. (e) P[-1.25 Z< 1.75]. (f) z.10- (g) Z,90 (h) The point z such that P[-z 1.57]. %3D that X is normałly distributed with u (a) What is the density for X? Sketch aʻgraph of the density function. Indicate on this graph the probability that X lies between 1.1 and 1.9. Find = 1.5 and o = .2 g/cm³.
OWAZ CONTINUOUS DISTRIBUTIONS 145 36. Rock noise in an underground mine occurs at an average rate of three per hour. (See Exercise 65, Chap. 3.) Find the probability that no rock noise will be recorded for at least 30 minutes. 37. California is hit every year by approximately 500 earthquakes that are large enough to be felt. However, those of destructive magnitude occur, on the av- erage, once a year. Find the probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs. (See Exercise 64, Chap. 3.) 38, Consider a chi-squared random variable with 15 degrees of freedom. (a) What is the mean of X?;? What is its variance? (b) What is the expression for the density for X75? (c) What is the expression for the moment generating function for X5? (d) Use Table IV of App. A to find each of the following: 2. P[6.26 < X{s < 27.5] - Xos P[Xis ¥ 5.23] P[X}s²22.3] 2 X95 15 Section 4.4 39. Use Table V of App. A to find each of the following: (a) P[Z< 1.57]. (c) P[Z = 1.57]. (e) P[-1.25 Z< 1.75]. (f) z.10- (g) Z,90 (h) The point z such that P[-z 1.57]. %3D that X is normałly distributed with u (a) What is the density for X? Sketch aʻgraph of the density function. Indicate on this graph the probability that X lies between 1.1 and 1.9. Find = 1.5 and o = .2 g/cm³.
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![OWAZ
CONTINUOUS DISTRIBUTIONS 145
36. Rock noise in an underground mine occurs at an average rate of three per
hour. (See Exercise 65, Chap. 3.) Find the probability that no rock noise will
be recorded for at least 30 minutes.
37. California is hit every year by approximately 500 earthquakes that are large
enough to be felt. However, those of destructive magnitude occur, on the av-
erage, once a year. Find the probability that at least 3 months elapse before the
first earthquake of destructive magnitude occurs. (See Exercise 64, Chap. 3.)
38, Consider a chi-squared random variable with 15 degrees of freedom.
(a) What is the mean of X?;? What is its variance?
(b) What is the expression for the density for X75?
(c) What is the expression for the moment generating function for X5?
(d) Use Table IV of App. A to find each of the following:
2.
P[6.26 < X{s < 27.5]
- Xos
P[Xis ¥ 5.23]
P[X}s²22.3]
2
X95
15
Section 4.4
39. Use Table V of App. A to find each of the following:
(a) P[Z< 1.57].
(c) P[Z = 1.57].
(e) P[-1.25 Z< 1.75]. (f) z.10-
(g) Z,90
(h) The point z such that P[-z<Z< z] = .95.
(i) The point z such that P[-zSZ< z] = ,90.
40. The bulk density of soil is defined as the mass of dry solids per unit bulk vol
ume. A high bulk density implies a compact soil with few pores. Bulk density
is an important factor in influencing root development, seedling emergence,
and aeration. Let X denote the bulk density of Pima clay loam. Studies show
(b) P[Z< 1.57].
(d) P[Z> 1.57].
%3D
that X is normałly distributed with u
(a) What is the density for X? Sketch aʻgraph of the density function. Indicate
on this graph the probability that X lies between 1.1 and 1.9. Find
= 1.5 and o = .2 g/cm³.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc074fc7e-4e48-46f1-bfc4-aee6ba4e6262%2Fdee8cc9a-8438-4ba6-aaee-009f4a9ae927%2Fmt1cls.jpeg&w=3840&q=75)
Transcribed Image Text:OWAZ
CONTINUOUS DISTRIBUTIONS 145
36. Rock noise in an underground mine occurs at an average rate of three per
hour. (See Exercise 65, Chap. 3.) Find the probability that no rock noise will
be recorded for at least 30 minutes.
37. California is hit every year by approximately 500 earthquakes that are large
enough to be felt. However, those of destructive magnitude occur, on the av-
erage, once a year. Find the probability that at least 3 months elapse before the
first earthquake of destructive magnitude occurs. (See Exercise 64, Chap. 3.)
38, Consider a chi-squared random variable with 15 degrees of freedom.
(a) What is the mean of X?;? What is its variance?
(b) What is the expression for the density for X75?
(c) What is the expression for the moment generating function for X5?
(d) Use Table IV of App. A to find each of the following:
2.
P[6.26 < X{s < 27.5]
- Xos
P[Xis ¥ 5.23]
P[X}s²22.3]
2
X95
15
Section 4.4
39. Use Table V of App. A to find each of the following:
(a) P[Z< 1.57].
(c) P[Z = 1.57].
(e) P[-1.25 Z< 1.75]. (f) z.10-
(g) Z,90
(h) The point z such that P[-z<Z< z] = .95.
(i) The point z such that P[-zSZ< z] = ,90.
40. The bulk density of soil is defined as the mass of dry solids per unit bulk vol
ume. A high bulk density implies a compact soil with few pores. Bulk density
is an important factor in influencing root development, seedling emergence,
and aeration. Let X denote the bulk density of Pima clay loam. Studies show
(b) P[Z< 1.57].
(d) P[Z> 1.57].
%3D
that X is normałly distributed with u
(a) What is the density for X? Sketch aʻgraph of the density function. Indicate
on this graph the probability that X lies between 1.1 and 1.9. Find
= 1.5 and o = .2 g/cm³.
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