If the weight (in grams) of cereal in a box of Lucky Charms is N(489,6), what is
ID: 3134748 • Letter: I
Question
If the weight (in grams) of cereal in a box of Lucky Charms is N(489,6), what is the probability that the box will contain less than the advertised weight of 464 gm? Note: You may need to use Excel to calculate the exact probabilities. (Round your answer to 5 decimal places.)If the weight (in grams) of cereal in a box of Lucky Charms is N(489,6), what is the probability that the box will contain less than the advertised weight of 464 gm? Note: You may need to use Excel to calculate the exact probabilities. (Round your answer to 5 decimal places.)
Explanation / Answer
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 464
u = mean = 489
s = standard deviation = 6
Thus,
z = (x - u) / s = -4.166666667
Thus, using a table/technology, the left tailed area of this is
P(z < -4.166666667 ) = 1.54543*10^-5 or 0.0000154543 [ANSWER]
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[You can use =NORMDIST(464, 489, 6, 1) to produce this.]