(a)A 100(1 − ?)% confidence interval for the mean ? of a normal population when the value of ? is known is given by x − z?/2 · ? n, x + z?/2 · ? n .Under the same conditions as those leading to the interval,P (X − ?) ?√n < 1.645 = 0.95.Use this to derive a one-sided interval for ? that has infinite width and provides a lower confidence bound on ?. x − 1.645? n, ∞ ∞, x + 1.645?n ∞, x − 1.645? n x + 1.645? n, ∞ x − 1.645?n, ∞ What is this interval for the true average porosity of a certain seam of coal samples that is normally distributed with true standard deviation 0.79 if the average porosity for 20 specimens from the seam was 4.85? (If you need to use or –, enter INFINITY or –INFINITY, respectively. Round your answers to four decimal places.) , (b)Generalize the result of part (a) to obtain a lower bound with confidence level 100(1 − ?)%. −x + z? ? n, ∞ −∞, x − z? ? n −∞, x + z? ? n x − z? ? n, ∞ x − z?, x + z? ? n (c)What is an analogous interval to that of part (b) that provides an upper bound on ?? −x + z? ? n, ∞ −∞, x − z? ? n −∞, x + z? ? n x − z? ? n, ∞ x − z?, x + z? ? n Compute this 99% interval for the true average stray-load loss ? (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1,500 rpm, when n = 25 and x = 58.3. Assume that stray-load loss is normally distributed with ? = 3.0. (If you need to use or –, enter INFINITY or –INFINITY, respectively. Round your answers to four decimal places.) , You may need to use the appropriate table in the Appendix of Tables to answer this question. (a) A 100(1 - a)% confidence interval for the mean u of a normal population when the value of o is known is given by+ Z a/2Under the same conditions as those leading to the interval,(X - µ)P< 1.645 = 0.95.VnUse this to derive a one-sided interval for u that has infinite width and provides a lower confidence bound on u.O(x - 1.645-00,,x + 1.645º)x - 1.645-1.645 )O (x + 1.645-00(7- 1.645 .x –, 00nWhat is this interval for the true average porosity of a certain seam of coal samples that is normally distributed with true standard deviation 0.79 if the average porosity for 20 specimens from the seam was4.85? (If you need to use o or -00, enter INFINITY or -INFINITY, respectively. Round your answers to four decimal places.) (b) Generalize the result of part (a) to obtain a lower bound with confidence level 100(1 – a)%.-x + Z-00,x --o,nх — Z(c) What is an analogous interval to that of part (b) that provides an upper bound on u?-x + z-00, X - Z.Vn-00, x + Z,VnE, 00z , X + za'Compute this 99% interval for the true average stray-load loss u (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1,500 rpm, when n = 25 and x = 58.3.Assume that stray-load loss is normally distributed with o = 3.0. (If you need to use co or -0o, enter INFINITY or -INFINITY, respectively. Round your answers to four decimal places.)You may need to use the appropriate table in the Appendix of Tables to answer this question.

Solution: Given information: n= 20 Sample size x = 4.85 Sample mean σ=0.79 Population standard…

Answered: 100(1 a)% confidence interval for the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

100%

(a)

A 100(1 − ?)% confidence interval for the mean ? of a normal population when the value of ? is known is given by

x − z_?/2 ·

, x + z_?/2 ·

Under the same conditions as those leading to the interval,

(X − ?)

√n

< 1.645

= 0.95.

Use this to derive a one-sided interval for ? that has infinite width and provides a lower confidence bound on ?.

x − 1.645

, ∞

∞, x + 1.645

∞, x − 1.645

x + 1.645

, ∞

x − 1.645

, ∞

What is this interval for the true average porosity of a certain seam of coal samples that is normally distributed with true standard deviation 0.79 if the average porosity for 20 specimens from the seam was 4.85? (If you need to use or –, enter INFINITY or –INFINITY, respectively. Round your answers to four decimal places.)

(b)

Generalize the result of part (a) to obtain a lower bound with confidence level

100(1 − ?)%.

−x + z_?

, ∞

−∞, x − z_?

−∞, x + z_?

x − z_?

, ∞

x − z_?, x + z_?

(c)

What is an analogous interval to that of part (b) that provides an upper bound on ??

−x + z_?

, ∞

−∞, x − z_?

−∞, x + z_?

x − z_?

, ∞

x − z_?, x + z_?

Compute this 99% interval for the true average stray-load loss ? (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1,500 rpm, when

n = 25

and

x = 58.3.

Assume that stray-load loss is normally distributed with

? = 3.0.

(If you need to use or –, enter INFINITY or –INFINITY, respectively. Round your answers to four decimal places.)

You may need to use the appropriate table in the Appendix of Tables to answer this question.

(a) A 100(1 - a)% confidence interval for the mean u of a normal population when the value of o is known is given by
+ Z a/2
Under the same conditions as those leading to the interval,
(X - µ)
P
< 1.645 = 0.95.
Vn
Use this to derive a one-sided interval for u that has infinite width and provides a lower confidence bound on u.
O(x - 1.645-
00,
,x + 1.645º)
x - 1.645-
1.645 )
O (x + 1.645-
00
(7- 1.645 .
x –
, 00
n
What is this interval for the true average porosity of a certain seam of coal samples that is normally distributed with true standard deviation 0.79 if the average porosity for 20 specimens from the seam was
4.85? (If you need to use o or -00, enter INFINITY or -INFINITY, respectively. Round your answers to four decimal places.)

(b) Generalize the result of part (a) to obtain a lower bound with confidence level 100(1 – a)%.
-x + Z
-00,
x -
-o,
n
х — Z
(c) What is an analogous interval to that of part (b) that provides an upper bound on u?
-x + z
-00, X - Z.
Vn
-00, x + Z,
Vn
E, 00
z , X + z
a'
Compute this 99% interval for the true average stray-load loss u (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1,500 rpm, when n = 25 and x = 58.3.
Assume that stray-load loss is normally distributed with o = 3.0. (If you need to use co or -0o, enter INFINITY or -INFINITY, respectively. Round your answers to four decimal places.)
You may need to use the appropriate table in the Appendix of Tables to answer this question.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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