Question

Any idea how to solve this?

Answer 1

\[P(57 \le X \le 67)\]

Answer 2

According to normal approximation?

Answer 3

This is applications on z-scores.

Answer 4

Yeah I know but which approximation are you being required to use?

Answer 5

Assume the random variable X is normally distributed with mean mu equals μ=50 and standard deviation sigma equals σ=7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

Answer 6

That's the whole question and figured out the shading. I don't know the solving area.

Answer 7

Okay now its clear.

Answer 8

So you only want to know how to convert X into z score?

Answer 9

Well solving the question what I posted above, yes. I do want to know how to do that:)

Answer 10

\[\large\rm z = \frac{X-Mean}{Standard~Deviation} \]

Answer 11

So now can you convert it into z scores?

Answer 12

\[\int\limits_{57}^{67} f(x) dx \] this low of probability i think

Answer 13

@YanaSidlinskiy

Answer 14

No, I need help throughout the whole problem and dinamix, I've never used that before so I want to stick with what I'm familiar with.

Answer 15

@dinamix That's wrong. Because the curve we are required to use is normal approximation curve and between 57 and 67 interval the area will be ~ 0.

Answer 16

So can you convert it into z-scores?

Answer 17

but when we use that ?

Answer 18

yup @FaiqRaees ok ty ;D i understand now

Answer 19

How would I figure out what's my x?

Answer 20

\[\large\rm P(57 \le X \le 67) \] 57 and 67 are your X

Answer 21

What? I'm really confused.

Answer 22

did you make a drawing ?

Answer 23

Yes, I did.

Answer 24

can you post it ?

Answer 25

Yes.

Answer 26

\[\large\rm P(57 \le X \le 67) \]
\[\large\rm P(\frac{57-50}{7} \le z \le \frac{67-50}{7} ) \]

Answer 27

ok, so the problem is to find the area of the blue region.
(the entire area under the bell curve is 1)

Answer 28

Ok.

Answer 29

The first step is translate the 57 to the "number of std dev" (from the mean of 50)
to do that, find the difference between 57 and 50

then divide by the std deviation. (you are figuring out "how many std deviations go into (57-50) "

Answer 30

I got 1.

Answer 31

now do the same for the upper bound of 67

Answer 32

I rounded to 2.4

Answer 33

ok, I would use 2.43

now we use an on-line calculator or a table to find the area.
what have you been using/studying ?

Answer 34

z-score tables but they all vary so I don't have a stable one to use for class.

Answer 35

they can be a bit tricky to use. can you post a link to one that you are using ?

Answer 36

Yes.

Answer 37

http://www.regentsprep.org/regents/math/algtrig/ats7/zchart.htm

Answer 38

ok. look in the positive section, for 1.0 and the column 0.0
what is the entry ?

Answer 39

.5398?

Answer 40

that is z= 0.1 (very close to the mean)
you want z= 1.0

Answer 41

Oh, sorry. Thanks for catchin that, hahha:)
.8413

Answer 42

yes, that looks good. the number 0.8413 is the area from the far left up to +1 std dev

next, we want the area up to 2.43

look for 2.4, then move sideways until you are in the 0.03 column
what do you get ?

Answer 43

.9925

Answer 44

yes, good job

Answer 45

So, that would be my final answer correct?

Answer 46

now we want the area between those 2 numbers
(big number - small number) will be the area in between. that is what we want.

Answer 47

So, between, 8413 and .9925 correct?

Answer 48

*.8413

Answer 49

yes, we want the difference

Answer 50

So wait, I would subtract those 2 numbers?

Answer 51

yes. It should make sense
we are doing this