Expert: Ahmed Salami - 10/27/2008

Question
The weight of a particular variety of orange is normally distributed with a mean of 155 grams and a standard deviation of 10 grams.

(a) Determine the proportion of oranges with weights between 145 grams and 165 grams.

(b) Determine the weight exceeded by 67 per cent of the oranges.


I WILL APPRECIATE YOUR HELP ON THIS ONE

Answer
Hi Syed,
The z statistic for any weight w is
z = (w - m)/s
where m is the mean and s is the standard deviation
For the weight 145 grams,
z = (145 - 155)/10
 = -10/10
 = -1
For the weight 165 grams,
z = (165 - 155)/10
 = 10/10
 = 1
The proportion of weights between 145 grams and 165 grams is the
area between z = -1 and z = 1, which from tables is 0.6827
Note that usual statistical tables gives you the area between 0 and z.
And A(-z) = -A(z), used because there are no areas(probabilities) for
negative values of z from the tables. Figure it out.

We need to find the weight such that the area to the right of its z
value is 0.67. From tables,
z = -0.44, but
z = (w - m)/s
-0.44 = (w - 155)/10
-4.4 = w - 155
w = 150.6 grams
Please let me know if you have any kind of problem with using the
table.

Regards.