Probability; help pls! Exercise 1: Let X be a random variable which, to each man sampled at random, associates his height in centimeters. We assume that X follows the normal distribution with mean 178 and standard deviation 10. Determine the probability of each of the following events: A: “A man taken at random has a height strictly greater than 180”. B: “A man taken at random has a height less than or equal to 150”. C: “A randomly selected man has a height between 160 and 185.”
Probability; help pls! Exercise 1: Let X be a random variable which, to each man sampled at random, associates his height in centimeters. We assume that X follows the normal distribution with mean 178 and standard deviation 10. Determine the probability of each of the following events: A: “A man taken at random has a height strictly greater than 180”. B: “A man taken at random has a height less than or equal to 150”. C: “A randomly selected man has a height between 160 and 185.”
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.3: Rates Of Change
Problem 6E: Find the average rate of change for each function over the given interval. y=3x2 between x=1 and x=2
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Exercise 1:
Let X be a random variable which, to each man sampled at random, associates his height in centimeters.
We assume that X follows the
- Determine the probability of each of the following
events:
A: “A man taken at random has a height strictly greater than 180”.
B: “A man taken at random has a height less than or equal to 150”.
C: “A randomly selected man has a height between 160 and 185.”
- Determine the real a such that P(X ≥ a) = 0, 2
- Determine the real b such that P(176 − b ≤ X ≤ 180 + b) = 0.68
Exercise 2:
Let X be a random density variable
f(x) = { e−2θx if x ≥ 0
0 else
- Find θ so that f is a probability density.
- Determine the distribution
function F of the variable X. - Calculate the expectation and variance of X.
- Let Y be the random variable defined by Y = θX. What is the law of Y?
Exercise 3:
In a garden center: 25% of the plants are less than a year old, 60% are 1 to 2 years old, 25% have yellow flowers, 60% have pink flowers, 15% have yellow flowers and less than a year old , 3% are more than 2 years old and have neither yellow nor pink flowers. 15% of those who are 1 to 2 years old have
yellow flowers, 15% of those 1-2 years old have neither yellow nor pink flowers. It is assumed that the flowers cannot be both yellow and pink at the same time. We choose a plant at random in this garden center.
- What is the probability that it is less than a year old and has pink flowers?
- What is the probability that she has pink flowers, given that she is over 2 years old?
- What is the probability that it is over two years old and has yellow flowers?
Transcribed Image Text:Loi Normale centrée réduite
Probabilité de trouver une valeur inférieure à x.
f(x)
X
ooooo
~OTN3 in 600
0,04
0,05
0,00
0,0 0,5000
0,07 0,08
0,5279 0,5319
0,5398
0,5675 0,5714
0,5793
0,6217
0,7852
0,7967
0,8238 0,8264
0,8133
0,8315 0,8340 0,8365 0,8389
0,8554 0,8577 0,8599
0,8621
0,8770 0,8790 0,8810
0,8830
0,8997
1,1
1,2
1,3
1,4
1,5
0,9162
0,9525 0,9535
0,01 0,02 0,03
0,06
0,5040 0,5080 0,5120 0,5160 0,5199 0,5239
0,5438 0,5478 0,5517 0,5557 0,5596 0,5636
0,2
0,5832 0,5871 0,5910 0,5948 0,5987 0,6026 0,6064 0,6103
0,3 0,6179
0,6255 0,6293 0,6331 0,6368 0,6406 0,6443 0,6480
0,4 0,6554 0,6591 0,6628
0,6664 0,6700 0,6736 0,6772 0,6808 0,6844
0,5 0,6915 0,6950 0,6985 0,7019 0,7054 0,7088 0,7123 0,7157 0,7190
0,6 0,7257 0,7291 0,7324 0,7357 0,7389 0,7422 0,7454 0,7486 0,7517
0,7 0,7580 0,7611 0,7642 0,7673 0,7704 0,7734 0,7764 0,7794 0,7823
0,8 0,7881 0,7910
0,7939
0,7995 0,8023 0,8051 0,8078 0,8106
0,9 0,8159 0,8186 0,8212
0,8289
1,0 0,8413
0,8438 0,8
0,8485 0,8508 0,8531
0,8643 0,8665 0,8686 0,8708 0,8729 0,8749
0,8849 0,8869 0,8888 0,8907 0,8925 0,8944 0,8962 0,8980
0,9032 0,9049 0,9066 0,9082 0,9099 0,9115 0,9131 0,9147
0,9192 0,9207 0,9222 0,9236 0,9251 0,9265
0,9332 0,9345
0,9357 0,9370 0,9382 0,9394
0,9452 0,9463 0,9474 0,9484 0,9495 0,9505
0,9554 0,9564 0,9573 0,9582 0,9591 0,9599
0,9641 0,9649 0,9656 0,9664 0,9671 0,9678
0,9713 0,9719 0,9726 0,9732 0,9738 0,9744
0,9750
0,9772 0,9778 0,9783 0,9788 0,9793 0,9798
0,9803
0,9821 0,9826 0,9830 0,9834 0,9838 0,9842 0,9846
0,9861 0,9864 0,9868
0,9871 0,9875 0,9878 0,9881
0,9893 0,9896 0,9898 0,9901 0,9904 0,9906 0,9909 0,9911 0,9913
0,9920 0,9922 0,9925 0,9927 0,9929 0,9931 0,9932 0,9934
0,9941 0,9943 0,9945 0,9946 0,9948 0,9949 0,9951
0,9955 0,9956 0,9957 0,9959 0,9960 0,9961
0,9966 0,9967 0,9968 0,9969 0,9970 0,9971
0,9975 0,9976 0,9977 0,9977 0,9978 0,9979
0,9982 0,9983 0,9984 0,9984 0,9985 0,9985 0,9986 0,9986
0,9987 0,9987 0,9988 0,9988 0,9989 0,9989 0,9989 0,9990 0,9990
0,9991 0,9991 0,9991 0,9992 0,9992 0,9992 0,9992 0,9993 0,9993
0,9993 0,9994 0,9994 0,9994 0,9994 0,9994 0,9995 0,9995 0,9995
0,9995 0,9995 0,9996 0,9996 0,9996 0,9996 0,9996 0,9996 0,9997
0,9997 0,9997 0,9997 0,9997 0,9997 0,9998
0,9998 0,9998 0,9998 0,9998 0,9998 0,9998
0,9279 0,9292 0,9306
0,9406 0,9418 0,9429
0,9515
0,9608 0,9616 0,9625
0,9686 0,9693 0,9699
0,9756 0,9761
0,9808 0,9812
2,2
0,9850 0,9854
0,9884 0,9887
2,3
2,4 0,9918
2,5 0,9938 0,9940
0,9962 0,9963
0,9972 0,9973
0,9979 0,9980
0,9981
0,9982
3,4 0,9997 0,9997 0,9997 0,9997
3,5 0,9998 0,9998 0,9998 0,9998
0,1
L3SSEN -
1,6
1,7
1,8
1,9
12 WN-00
2,0
NNNN
2,1
NN
67890FNME
2,6 0,9953
0,9965
2,8 0,9974
NNN
2,7
N3333505
2,9 0,9981
3,0 0,9987
3,1 0,9990
3,2 0,9993
3,3 0,9995
X
Table pour les grandes valeurs de x:
3,2
3,4
+50
3,6
F(x)= [² e du
2π
3,8
0,09
0,5359
0,5753
0,6141
0,6517
0,6879
4,4
0,7224
0,7549
0,9015
0,9177
0,9319
0,9441
0,9545
0,9633
0,9706
0,9767
0,9817
0,9857
0,9890
0,9916
x
4,2
4,6
F(x) 0,99865003 0,99931280 0,99966302 0,99984085 0.99992763 0,99996831 0,999986650,99999458 0,999997890,99999921
0,9936
0,9952
0,9964
0,9974
4,8
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Probability; help pls!
Exercise 1:
Let X be a random variable which, to each man sampled at random, associates his height in centimeters.
We assume that X follows the
- Determine the probability of each of the following
events:
A: “A man taken at random has a height strictly greater than 180”.
B: “A man taken at random has a height less than or equal to 150”.
C: “A randomly selected man has a height between 160 and 185.”
- Determine the real a such that P(X ≥ a) = 0, 2
- Determine the real b such that P(176 − b ≤ X ≤ 180 + b) = 0.68
Transcribed Image Text:Loi Normale centrée réduite
Probabilité de trouver une valeur inférieure à x.
f(x)
X
ooooo
~OTN3 in 600
0,04
0,05
0,00
0,0 0,5000
0,07 0,08
0,5279 0,5319
0,5398
0,5675 0,5714
0,5793
0,6217
0,7852
0,7967
0,8238 0,8264
0,8133
0,8315 0,8340 0,8365 0,8389
0,8554 0,8577 0,8599
0,8621
0,8770 0,8790 0,8810
0,8830
0,8997
1,1
1,2
1,3
1,4
1,5
0,9162
0,9525 0,9535
0,01 0,02 0,03
0,06
0,5040 0,5080 0,5120 0,5160 0,5199 0,5239
0,5438 0,5478 0,5517 0,5557 0,5596 0,5636
0,2
0,5832 0,5871 0,5910 0,5948 0,5987 0,6026 0,6064 0,6103
0,3 0,6179
0,6255 0,6293 0,6331 0,6368 0,6406 0,6443 0,6480
0,4 0,6554 0,6591 0,6628
0,6664 0,6700 0,6736 0,6772 0,6808 0,6844
0,5 0,6915 0,6950 0,6985 0,7019 0,7054 0,7088 0,7123 0,7157 0,7190
0,6 0,7257 0,7291 0,7324 0,7357 0,7389 0,7422 0,7454 0,7486 0,7517
0,7 0,7580 0,7611 0,7642 0,7673 0,7704 0,7734 0,7764 0,7794 0,7823
0,8 0,7881 0,7910
0,7939
0,7995 0,8023 0,8051 0,8078 0,8106
0,9 0,8159 0,8186 0,8212
0,8289
1,0 0,8413
0,8438 0,8
0,8485 0,8508 0,8531
0,8643 0,8665 0,8686 0,8708 0,8729 0,8749
0,8849 0,8869 0,8888 0,8907 0,8925 0,8944 0,8962 0,8980
0,9032 0,9049 0,9066 0,9082 0,9099 0,9115 0,9131 0,9147
0,9192 0,9207 0,9222 0,9236 0,9251 0,9265
0,9332 0,9345
0,9357 0,9370 0,9382 0,9394
0,9452 0,9463 0,9474 0,9484 0,9495 0,9505
0,9554 0,9564 0,9573 0,9582 0,9591 0,9599
0,9641 0,9649 0,9656 0,9664 0,9671 0,9678
0,9713 0,9719 0,9726 0,9732 0,9738 0,9744
0,9750
0,9772 0,9778 0,9783 0,9788 0,9793 0,9798
0,9803
0,9821 0,9826 0,9830 0,9834 0,9838 0,9842 0,9846
0,9861 0,9864 0,9868
0,9871 0,9875 0,9878 0,9881
0,9893 0,9896 0,9898 0,9901 0,9904 0,9906 0,9909 0,9911 0,9913
0,9920 0,9922 0,9925 0,9927 0,9929 0,9931 0,9932 0,9934
0,9941 0,9943 0,9945 0,9946 0,9948 0,9949 0,9951
0,9955 0,9956 0,9957 0,9959 0,9960 0,9961
0,9966 0,9967 0,9968 0,9969 0,9970 0,9971
0,9975 0,9976 0,9977 0,9977 0,9978 0,9979
0,9982 0,9983 0,9984 0,9984 0,9985 0,9985 0,9986 0,9986
0,9987 0,9987 0,9988 0,9988 0,9989 0,9989 0,9989 0,9990 0,9990
0,9991 0,9991 0,9991 0,9992 0,9992 0,9992 0,9992 0,9993 0,9993
0,9993 0,9994 0,9994 0,9994 0,9994 0,9994 0,9995 0,9995 0,9995
0,9995 0,9995 0,9996 0,9996 0,9996 0,9996 0,9996 0,9996 0,9997
0,9997 0,9997 0,9997 0,9997 0,9997 0,9998
0,9998 0,9998 0,9998 0,9998 0,9998 0,9998
0,9279 0,9292 0,9306
0,9406 0,9418 0,9429
0,9515
0,9608 0,9616 0,9625
0,9686 0,9693 0,9699
0,9756 0,9761
0,9808 0,9812
2,2
0,9850 0,9854
0,9884 0,9887
2,3
2,4 0,9918
2,5 0,9938 0,9940
0,9962 0,9963
0,9972 0,9973
0,9979 0,9980
0,9981
0,9982
3,4 0,9997 0,9997 0,9997 0,9997
3,5 0,9998 0,9998 0,9998 0,9998
0,1
L3SSEN -
1,6
1,7
1,8
1,9
12 WN-00
2,0
NNNN
2,1
NN
67890FNME
2,6 0,9953
0,9965
2,8 0,9974
NNN
2,7
N3333505
2,9 0,9981
3,0 0,9987
3,1 0,9990
3,2 0,9993
3,3 0,9995
X
Table pour les grandes valeurs de x:
3,2
3,4
+50
3,6
F(x)= [² e du
2π
3,8
0,09
0,5359
0,5753
0,6141
0,6517
0,6879
4,4
0,7224
0,7549
0,9015
0,9177
0,9319
0,9441
0,9545
0,9633
0,9706
0,9767
0,9817
0,9857
0,9890
0,9916
x
4,2
4,6
F(x) 0,99865003 0,99931280 0,99966302 0,99984085 0.99992763 0,99996831 0,999986650,99999458 0,999997890,99999921
0,9936
0,9952
0,9964
0,9974
4,8
Solution
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