Question

I hope some one can help me!
The mean midday temperature recorded in June in a city in South California is 36ºC, and the standard deviation is 3ºC.
Assuming the data is normally distributed, the number of days in June when the midday temperature was between 39ºC and 42ºC is?

Answer 1

standard deviation is 3 so it is 99.7%

Answer 2

26-3=33
36+3=39
3/sqrt+(36)=1/2 = 0.5

Answer 3

@jim_thompson5910 can u help please?

Answer 4

x = 39
z = (x-mu)/sigma
z = (39-36)/3
z = 3/3
z = 1

So when the raw score is x = 39, the z score is z = 1

-------------------------------------------------------

x = 42
z = (x-mu)/sigma
z = (42-36)/3
z = 6/3
z = 2

So when the raw score is x = 42, the z score is z = 2

Answer 5

What is the area under the standard normal distribution curve from z = 1 to z = 2 ?

Answer 6

68

Answer 7

Are you talking about the empirical rule?

Answer 8

is that the z curve?

Answer 9

I thought the difference was 1 under normal distribution but i still dont get this.

Answer 10

do you have z table with you? or a TI calculator?

Answer 11

no just online one

Answer 12

ok let's use this table

https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf

Answer 13

locate the row that has 1.0

locate the column that has .00

what is in that row/column combo?

Answer 14

0.8413

Answer 15

So

P(Z < 1) = 0.8413

Answer 16

what is the value of P(Z < 2) ?

Answer 17

im trying to figure that out

Answer 18

use the table

locate 2.00

Answer 19

0.9773

Answer 20

P(Z < 2)=0.9773

Answer 21

this is hard

Answer 22

now what do I do?

Answer 23

you now subtract the two values

Answer 24

0.9773 - 0.8413 = 0.136

Answer 25

So P( 1 < Z < 2 ) = 0.136

Answer 26

So roughly 13.6% of the values are between z = 1 and z = 2

Answer 27

which means 13.6% of the days in June are going to have days with temps between 39 degrees C and 42 degrees C

Answer 28

my answers to choose are 3, 4, 7, or 12

Answer 29

how many days are in June?

Answer 30

i would have to choose 12 then. I think 30

Answer 31

30 days in june

13.6% of 30 = ???

Answer 32

so it would be 4

Answer 33

yes

Answer 34

crazy how do you know and remember this. so hard. thank you!

Answer 35

with more practice, it should come easier

Answer 36

wow I hope so thanks