# mean and standard deviation

• Jun 19th 2008, 12:47 PM
roxy
mean and standard deviation
I have scanned over and over a similar problem on the forum, i just cannot understand.
I understand that i am to read the normal Z tables like a stem plot but cannot find any connection to the answers given.

Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation 120g. Let X be the weight of a bucket in a randomly chosen batch.
Mean- 1250 Std. dev = 120

(a) Find Pr(X > 1250) This is the mean so prob has to equal half... (0.5)

(b) Find Pr(1250 < X < 1380)
= Find Z first z = 1380 – 1250 / 120 = 130/120 = 1.083
Pr(1250 < X < 1380) = look up z in tables

(c) Find Pr(1135 < X < 1275)
= Find Z (you need 2 values – lower should work out as -0.958 and upper as 0.208)tutor notes
= Pr(1135 < X < 1275) = look up Z values in tables and add together
It is spelled out for me, i cant see where to go. how to get the Z,
• Jun 19th 2008, 01:09 PM
Moo
Hello,

Quote:

Originally Posted by roxy
I have scanned over and over a similar problem on the forum, i just cannot understand.
I understand that i am to read the normal Z tables like a stem plot but cannot find any connection to the answers given.

Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation 120g. Let X be the weight of a bucket in a randomly chosen batch.
Mean- 1250 Std. dev = 120

(a) Find Pr(X > 1250) This is the mean so prob has to equal half... (0.5)

(b) Find Pr(1250 < X < 1380)
= Find Z first z = 1380 – 1250 / 120 = 130/120 = 1.083
Pr(1250 < X < 1380) = look up z in tables

(c) Find Pr(1135 < X < 1275)
= Find Z (you need 2 values – lower should work out as -0.958 and upper as 0.208)tutor notes
= Pr(1135 < X < 1275) = look up Z values in tables and add together
It is spelled out for me, i cant see where to go. how to get the Z,

The z-table is made up for a standard normal distribution..

So for a random variable X that has a normal distribution, a mean of $\mu$ and a standard dev of $\sigma$, there is Z that has a standard normal distribution :

$Z=\frac{X-\mu}{\sigma}$

So transform $P(1250 $=P(0

Same for $P(1135 $-P(-0.9583 $=P(Z<0.2083)-(1-P(Z<-0.9583))=P(Z<0.2083)+P(Z<-0.9583)-1$
• Jun 19th 2008, 01:15 PM
galactus
Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation
(c) Find Pr(1135 < X < 1275)
= Find Z (you need 2 values – lower should work out as -0.958 and upper as 0.208)tutor notes
= Pr(1135 < X < 1275) = look up Z values in tables and add together
It is spelled out for me, i cant see where to go. how to get the Z,[/quote]

For this one fins the two z-score, then look them up to see what probability corresponds.

$z=\frac{x-{\mu}}{\sigma}$

$-.958=\frac{1135-1250}{120}$

Look up in the table and we get .169

$.208=\frac{1275-1250}{120}$

Look up in the table and we get .582

Subtract and we get a probability of .413
• Jun 20th 2008, 12:27 AM
roxy
Thankyou, i will have a look at all the info you sent. sorry i cant give you chocolates, maybe virtual.
• Jun 20th 2008, 01:10 PM
roxy
still stuck
http://www.mathhelpforum.com/math-he...68ea1172-1.gif

Look up in the table and we get .169

http://www.mathhelpforum.com/math-he...d129a200-1.gif

Look up in the table and we get .582

Subtract and we get a probability of .413 _

this .169 and .582 is where i am having trouble. when i look the .958 up in the z tables all i get is .3309 . when i look up z= .208 i find .824