Statistical Inference

[Eugene99]

Question 20:
μ=29 , σ=5
a)
Z(30) = (30-29)/5 = 0.2 from the table: 0.5793
Z(34) = (34-29)/5 = 1 from the table: 0.8413

30>Z>35 : 0.8413 - 0.5793
= 0.262

b)
At least 23 million means Z >23
Z(23) = (23-29)/5 = -1.2
from the table: 0.8849
cuz the value was negative, 1- 0.8849
= 0.1151
since we were to find Z>23, simply subtract from 1 :
1 -0.1151
=0.8849

c)
Z>40
Z(40) = (40-29)/ 5 = 2.2
= 0.9861
1- 0.9861 = 0.014
__________________________________________________________________________________________________
Hope I'm doin them right

 

[deelaw007]

Question 19:
μ=2708, σ=650
a)
Z(3000) = (3000-2708)/650 = 0.4492 from the table: 0.4492: 0.6736
1-0.6736
= 0.326
For percentage, just multiply the probability by 100
0.326 will be 32.6%

b)
We already found Z(3000) in the previous part, so,
Z(3500) = (3500-2708)/650 = 1.21
1.21 from the table: 0.8869
between 3000 and 3500: 0.8869 - 0.6736
= 0.2133
= 21.33%

c) Z(2500) = (2500-2708)/ 650 = -0.32
0.32 from the table is 0.6255
since it was negative value we subtract from 1 :
1-0.6255
= 0.3745
We already found Z(3500) in previous part, which was 0.8869
Between 3500 and 2500:
0.8869 - 0.3745
= 0.514
or say 51.4%

no no its alright!
Fine

 

[Eugene99]

Question 21:
μ=15 , σ=3.5
a)
Z>20 :
Z(20)= (20-15)/3.5 = 1.42 from the table: 0.9222
1-0.9222
=0.078

b)
Z<20
we already found that in previous part : 0.9222

c)
Z(10)= (10-15)/3.5 = -1.42
1.42 is 0.9222 from the table
1-0.9222
=0.078
Z(12) = 12-15/3.5 = -0.85
prob from the table at 0.85: 0.8023
1-0.8023 (cuz it was a negative value)
=0.1977
Now between 10 and 12:
0.1977-0.078
= 0.1197

 

[Eugene99]

Question 22:
μ=38.3 , σ=7.5
a)
Z<30 :
Z(30)= (30-38.3)/7.5 = -1.106
prob at 1.106: 0.8643
1-0.8643
=0.135
or 13.5%

b)
Z(35)
Z(35)= (35-38.3)/7.5 = -0.44
prob at 0.44: 0.6700
1-0.6700
= 0.33
Z(30) we alrady found
so between 30 and 35:
0.33-0.135
= 0.195 or 19.5%

c)
Z(40)= (40-38.3)/7.5 = 0.2
prob at 0.2: 0.5793
0.5793-0.135
= 0.4443
or 44.43%
______________________________________________________________________________
My God! they are tiresome!!

 

[deelaw007]

Question 22:
μ=38.3 , σ=7.5
a)
Z<30 :
Z(30)= (30-38.3)/7.5 = -1.106
prob at 1.106: 0.8643
1-0.8643
=0.135
or 13.5%

b)
Z(35)
Z(35)= (35-38.3)/7.5 = -0.44
prob at 0.44: 0.6700
1-0.6700
= 0.33
Z(30) we alrady found
so between 30 and 35:
0.33-0.135
= 0.195 or 19.5%

c)
Z(40)= (40-38.3)/7.5 = 0.2
prob at 0.2: 0.5793
0.5793-0.135
= 0.4443
or 44.43%
______________________________________________________________________________
My God! they are tiresome!!

Thanks
just stop its donenow

 

[Eugene99]

sorry for the mess

 

[deelaw007]

And q42 also

 

[Eugene99]

And q42 also

there is no Q42!

 

[deelaw007]

Wait

 

[Eugene99]

Wait

okay, tomorrow, right?

 

[deelaw007]

okay, tomorrow, right?

Yes

 

[deelaw007]

Solve this. Q37 and q42

 

[Eugene99]

Solve this. Q37 and q42

answers please

 

[deelaw007]

answers please

no answer :3

 

[deelaw007]

View attachment 59804 View attachment 59805 View attachment 59806 View attachment 59807 View attachment 59808 View attachment 59809

sorry for the mess

how did you get 0.8416 in Q 24?

 

[Eugene99]

how did you get 0.8416 in Q 24?

We are finding z value for 0.8. Find in the table where 0.8 is not the 0.8 in the right most row (that's the z-value) we have the x value and we have to correspond that to the z-value and see which z-value it coresponds to:
See in the red box 0.7995, that's the nearest to 0.8 we have got in the table. Which value of z it corresponds to? 0.8 (look in the green box), that means our answer is 0.8 something, but look above 0.7995 (green box) it's our 2nd digit, now we have 0.84 , but we still need to add 0.005 to get our correct value 0.8, right? so in the ADD table (it's for our 3rd digit 0.00x), we see adding 0.005 corresponds to 2 (the green box)
Now collect the final answer it's 0.842. (I wrote that wrong as 0.8416, though it rounds up to 0.842 so it didn't affect the answer)

Did you get that?

 

[deelaw007]

We are finding z value for 0.8. Find in the table where 0.8 is not the 0.8 in the right most row (that's the z-value) we have the x value and we have to correspond that to the z-value and see which z-value it coresponds to:View attachment 59847
See in the red box 0.7995, that's the nearest to 0.8 we have got in the table. Which value of z it corresponds to? 0.8 (look in the green box), that means our answer is 0.8 something, but look above 0.7995 (green box) it's our 2nd digit, now we have 0.84 , but we still need to add 0.005 to get our correct value 0.8, right? so in the ADD table (it's for our 3rd digit 0.00x), we see adding 0.005 corresponds to 2 (the green box)
Now collect the final answer it's 0.842. (I wrote that wrong as 0.8416, though it rounds up to 0.842 so it didn't affect the answer)

Did you get that?

why to add 5?

 

[deelaw007]

can u do Q28?

 

[Eugene99]

why to add 5?

Without that we have z-value for 0.7995 not 0.8. We need the value for 0.8. Add 0.005 to 0.7995 in your calc, you'll get 0.8, which is the value we are looking for. So if we add a 3rd digit of 5 in the z-value, it will get us 0.8 exactly

 

[Eugene99]

can u do Q28?

yes sure, I just did 42, let me post that first