1. ## mean and sd

Hiya...

The weights of cans of pears produced by a local canning factory are normally distributed with a mean of 500 grams and a standard deviation of 25 grams. Calculate the percentage of cans that weigh:

a. 430 grams or less.
b. between 525 and 550 grams.

Thanks!

2. Originally Posted by bennyya

b. between 525 and 550 grams.
The probability between 500 and 550 is 47.5% (2 standard deviations)
The probability between 500 and 525 is 34% (1 standard deviation)
Thus,
Probability between 525 and 550 is 47.5%-34%=13.5%

3. correct me if i'm wrong but i think you can do this with the Texas Instruments Ti-83 calc.
for question A)
if you go 2nd->DISTR (above VARS) -> 2: normalCdf (-1*10^99, 430, 500, 25)
it will give you roughly 0.0026 which is 0.256% of cans will be 430 grams or less.
Its a very small number, but dont forget its almost 3 std. dev's off the mean.
if it were 3 std. dev's off the mean it would have a probability of (1 - 0.997)/2 = 0.0015 = 0.15%.

Hope this helps