probability

Boxes of Bran Flakes are known to be normally distributed with a mean wieght of 475g and a standard deviation of 10g.
Calculate the probability of a box having a weight exceeding 485g.
Z=(X-mean)/sd
Z=(485-475)/10
Z=10/10
Z=1
Not sure where to go from here.....how do i read the z table?
So therefore the probability would be____?

Calculate the probability that a mean wieght of 16 boxes will exceed 480g
Z=(X-mean)/(sd/√16)
Z=(480-475)/(10/√16)Z=10/(10/4)
Z=10/2.5
Z=4
So therefore probability would be ____?

Sue0113 said:

Boxes of Bran Flakes are known to be normally distributed with a mean wieght of 475g and a standard deviation of 10g.
Calculate the probability of a box having a weight exceeding 485g.
Z=(X-mean)/sd
Z=(485-475)/10
Z=10/10
Z=1

Use the right-hand table for Z-scores. On the periphery, locate z = 1.00.
Read the 4 decimal place probability for that. That is the area up to
that z-score.
You want the area to the right of that z-score (because of the word
"exceeding"). Subtract the prior decimal from 1 for the desired probability.

Not sure where to go from here.....how do i read the z table?
So therefore the probability would be____?

Calculate the probability that a mean wieght of 16 boxes will exceed 480g
Z=(X-mean)/(sd/√16)
Z=(480-475)/(10/√16)
Z=10/(10/4) . . . . . . This should be 5/(10/4).
Z=10/2.5 . . . . . . This should be 5/2.5.
Z=4 . . . . . . This should be 2.

With this different (corrected) z-score, use the method in the prior
problem to work out the probability.

So therefore probability would be ____?

Click to expand...

...

So then the corrected answers would be

a)Z=1-.8413
Z= .1587
Therefore the probability of a box of cereal having a wieght exceeding 485g is .1587.

b) Z= 1-.9772
Z=.0228
Therefore the probability of the mean wieght of 16 boxes will exceed 480g is .0228.

Sue0113 said:

a)Z=1-.8413

<No, Z = 1. The probability that corresponds to that is 0.8413.>
Z= .1587
Therefore the probability of a box of cereal having a wieght exceeding 485g is 0.1587.

b) Z= 1-.9772 <No, Z = 2. The probability that corresponds to that is 0.9772.>
Z=.0228
Therefore the probability of the mean wieght of 16 boxes will exceed 480g is 0.0228.

Click to expand...

Z = 1.00

The entry for the probability in the Z Chart for that number is 0.8413.

Then 1 - 0.8413 = 0.1587 is the desired probability.

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The same setup that I showed for a) applies to b).

confused with your reply

So my answer is not correct, but I don't understand why it is not. A is correct but b is not? why is that?

Sue0113 said:

So my answer is not correct, but I don't understand why it is not. A is correct but b is not? why is that?

Click to expand...

No, neither of your answers are correct, because you typed that Z equals the probabilities.

You have to call something the right thing.
Your probabilities for both a and b are correct, though.


A Z-score is not a probability.

After you type "Z = (whatever)," then you would type something similar to

"Probability = (this)."

Your .1587 and .0228 are correct probabilities, but they are not Z-values.

A probability (or area under the bell-shaped curve) corresponds to a Z-value,

but they are not the same thing.

Thanks

Thanks for the clarification!