What is the standard deviation of this distribution?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
I'm confused by my professors work and how they got their answer in the example problem below. I attached part of the z table we're using because I couldn't add any more images. Thanks in advance.
Transcribed Image Text:2. The lengths of the leaves on a tree have an approximately normal distribution
with mean 10 cm. Thirty-seven percent of the leaves on the tree are over 12 cm
long. What is the standard deviation of this distribution?
3. Repeated weighings of the same object made by a scale have an approximately
normal distribution with standard deviation .05 grams. Seventy-five percent of
the weights are under 83 grams. What is the mean of this scale's reported
weights of this object?
u=10
J= .05
1637/+ for 6300,2 = .33= 12-10 =0=120 = 6.06cm
10 12
6300
1500
83
for 1500, z = .67= 8,3344 7 (61) (05)=8371
.05
⇒μ=83-(05).67)=(82.96659
Transcribed Image Text:Table Z
Areas under the
standard normal curve
Z
0
0.09 0.08 0.07 0.06
Second decimal place in z
0.05 0.04 0.03
0.02
0.0233 0.0239 0.0244 0.0250
0.0294 0.0301 0.0307 0.0314
0.0367 0.0375 0.0384 0.0392
0.0455 0.0465 0.0475 0.0485
0.0559 0.0571 0.0582 0.0594
0.01
0.00
0.0001
0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 -3.6
0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 -3.5
Z
0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 -3.4
0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005 -3.3
0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007 0.0007 -3.2
0.0007 0.0007 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009 0.0010 -3.1
0.0010 0.0010 0.0011 0.0011 0.0011 0.0012 0.0012 0.0013 0.0013 0.0013 -3.0
0.0681 0.0694 0.0708 0.0721 0.0735 0.0749
0.0823 0.0838 0.0853 0.0869 0.0885 0.0901
0.0985 0.1003 0.1020 0.1038 0.1056 0.1075
0.1170 0.1190 0.1210 0.1230 0.1251 0.1271
0.1379 0.1401 0.1423 0.1446 0.1469 0.1492
0.0000-3.9
0.0001 -3.8
0.0001 -3.7
0.0014 0.0014 0.0015 0.0015 0.0016 0.0016 0.0017 0.0018 0.0018 0.0019 -2.9
0.0019 0.0020 0.0021 0.0021 0.0022 0.0023 0.0023 0.0024 0.0025 0.0026 -2.8
0.0026 0.0027 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035 -2.7
0.0036 0.0037 0.0038 0.0039 0.0040 0.0041 0.0043 0.0044 0.0045 0.0047 -2.6
0.0048 0.0049 0.0051 0.0052 0.0054 0.0055 0.0057 0.0059 0.0060 0.0062 -2.5
0.1611 0.1635 0.1660 0.1685 0.1711 0.1736
0.1867 0.1894 0.1922 0.1949 0.1977 0.2005
0.2148 0.2177 0.2206 0.2236 0.2266 0.2296
0.2451 0.2483 0.2514 0.2546 0.2578 0.2611
0.2776 0.2810 0.2843 0.2877 0.2912 0.2946
0.0064 0.0066 0.0068 0.0069 0.0071 0.0073 0.0075 0.0078 0.0080 0.0082 -2.4
0.0084 0.0087 0.0089 0.0091 0.0094 0.0096 0.0099 0.0102 0.0104 0.0107 -2.3
0.0110 0.0113 0.0116 0.0119 0.0122 0.0125 0.0129 0.0132 0.0136 0.0139 -2.2
0.0143 0.0146 0.0150 0.0154 0.0158 0.0162 0.0166 0.0170 0.0174 0.0179 -2.1
0.0183 0.0188 0.0192 0.0197 0.0202 0.0207 0.0212 0.0217 0.0222 0.0228 -2.0
0.0256 0.0262 0.0268 0.0274 0.0281 0.0287 -1.9
0.0322 0.0329 0.0336 0.0344 0.0351 0.0359 -1.8
0.0401 0.0409 0.0418 0.0427 0.0436 0.0446 -1.7
0.0495 0.0505 0.0516 0.0526 0.0537 0.0548 -1.6
0.0606 0.0618 0.0630 0.0643 0.0655 0.0668 -1.5
0.0764 0.0778 0.0793 0.0808 -1.4
0.0918 0.0934 0.0951 0.0968 -1.3
0.1093 0.1112 0.1131 0.1151 -1.2
0.1292 0.1314 0.1335 0.1357 -1.1
0.1515 0.1539 0.1562 0.1587 -1.0
0.1762 0.1788 0.1814 0.1841 -0.9
0.2033 0.2061 0.2090 0.2119 -0.8
0.2327 0.2358 0.2389 0.2420 -0.7
0.2643 0.2676 0.2709 0.2743 -0.6
0.2981 0.3015 0.3050 0.3085 -0.5
0.3121 0.3156 0.3192 0.3228 0.3264 0.3300 0.3336 0.3372 0.3409 0.3446 -0.4
0.3483 0.3520 0.3557 0.3594 0.3632 0.3669 0.3707 0.3745 0.3783 0.3821 -0.3
0.3859 0.3897 0.3936 0.3974 0.4013 0.4052 0.4090 0.4129 0.4168 0.4207 -0.2
0.4247 0.4286 0.4325 0.4364 0.4404 0.4443 0.4483 0.4522 0.4562 0.4602 -0.1
0.4641 0.4681 0.4721 0.4761 0.4801 0.4840 0.4880 0.4920 0.4960 0.5000 -0.0
*For z ≤ -3.90, the areas are 0.0000 to four decimal places.
Expert Solution
Step 1
2. Let X be the random variable for the length of the leaves on a tree.
It has an approximately Normal distribution with a mean = 10 cm.
To find the std. dev. of the variable.
3. Let X be the random variable of weighing of the same object.
Given that,
sd = 0.05 grams
To find the mean of the distribution.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman