Can you explain why , so I understand?

2) A normal distribution has a mean of 102 and a standard deviation of 2.9.

What is the z-score of 105?

Enter your answer, rounded to the nearest hundredth.

Answer is 1.03

jjennylove Apr 5, 2019

#1**+2 **

Don't know about the first....but......here's the second one....

[ 105 - 102 ]

__________ =

2.9

3

____ =

2.9

1.03

CPhill Apr 5, 2019

#3**+2 **

[ 165 - 176 ]

_________ = z score we are looking for

11.4

-11

____ ≈ -.96

11. 4

Looking at the table here : http://www.z-table.com/

This corresponds to .1685

So....about 16.85% of the 120 will weigh < 165 lbs

So.....this means that 120 ( 1 - .1685) ≈ 99.78 will weigh > 165 lbs

So 99.78 will round to 100

Good job !!!

CPhill Apr 5, 2019

#4**0 **

Im so glad Im understanding these! Im going to be uplaoding more to double check not sure if you would like to but if you do that would be great.

Here is another one.

Now this one I was a bit confused but maybe I did it correctly

jjennylove
Apr 5, 2019

#5**0 **

I got 68.08 but what does this mean exactly ? That all the scores are below 68 ?

jjennylove
Apr 5, 2019

#8**+2 **

16% corresponds to either a z score of -.99 OR a z score of 1

So we either have that

[ score - 76 ]

___________ = -.99 multiply both sides by 8

8

score - 76 = -7.92 add 76 to both sides

score = 68.08......which means that 16% will be below about 68

OR

[ score - 76 ]

__________ = 1 multiply both sides by 8

8

score - 76 = 8 add 76 to both sides

score = 84 .....this means that 16% will be above 84

But...since this isn't one of your choices......68 is correct

[ Note that the 16% could be anywhere. for example....it could also mean the 16% "cluster" on either side of the mean ]

CPhill
Apr 5, 2019

#12**0 **

Since your online again, I was kind of confused on this one as to why you said " Since this isnt your choice it is 68"

jjennylove
Apr 5, 2019

#6**+2 **

OK

30% = .30 which corresponds to a z score ≈ -.52

So....we have

[ weight we are looking for - mean ]

_____________________________ = -.52

std dev

[ weight we are looking for - 143 ]

___________________________ = -.52 multiply both sides by 4.2

4.2

weight we are looking for - 143 = -2.184 add 143 to oth sides

weight we are looking for = 140.8 g (round to 141 g )

Good JOB !!!....I think you got it !!!

CPhill Apr 5, 2019

#7**+1 **

Yay! I am so happy im understanding it thank you for your detialed explanations !

jjennylove
Apr 5, 2019

#9**+1 **

I see it now! That was a confusing but from your explaintions it makes more sense. Thank you for your help CPhill

jjennylove
Apr 5, 2019

#10**+1 **

OK.....glad to help.....sorry I don't know the answer(s) to the first one....I hate to "guess" and maybe give incorrect answers......

CPhill
Apr 5, 2019

#11**+1 **

No its okay you have been plenty of help maybe ElectricPavlov can help me on it when he gets online. Im gonna repost the question in case he doesnt see it here. Thank you again

jjennylove
Apr 5, 2019