A company sells cookies in 250-gram packs. When a particular batch of 1,000 packs was weighed, the mean weight per pack was 255
grams and the standard deviation was 2.5 grams.Assuming the data is normally distributed, we can conclude that ___% of the packs weighed less than 250 grams
The expected value of the cookie pack is 250 g. From the 1000 packs sampled, the average weight was actually 255 g with a standard deviation of 2.5 g. That means, the z-score for this distribution is
z = (250 - 255)/2.5 = -2
Now, we're looking for the percentage or P-value for the packs that weigh less than 250 grams. Using the P-value table, we have
P(z < -2) = 1- P(z < z ) = 1- 0.9772 = 0.0228
Thus, the 2%<span> of the sample weighs less than 250 grams.
</span>
