A package of Toys Galore Cereal is marked "Net Wt. 12 oz." The actual weight is normally distributed, with a mean of 12 oz and a variance of 0.16.
(a) What percent of the packages will weigh less than 12 oz?
50
Correct: Your answer is correct.
%
(b) What weight will be exceeded by 2.3% of the packages? (Round your answer to one decimal place.)
12
Incorrect: Your answer is incorrect.
oz
3 answers
12 is correct
it is 12.4
You are correct. To find the weight that will be exceeded by 2.3% of the packages, you need to find the z-score that corresponds to the 2.3% percentile using a standard normal distribution table or calculator.
The z-score corresponding to the 2.3% percentile is approximately -1.81.
Then, you can use the formula:
z = (x - μ) / σ
where x is the weight you want to find, μ is the mean weight (12 oz), and σ is the standard deviation (which is the square root of the variance = 0.4 oz).
Plugging in the values:
-1.81 = (x - 12) / 0.4
Solving for x:
x = -1.81 * 0.4 + 12 = 11.276
Rounding to one decimal place, the weight that will be exceeded by 2.3% of the packages is 11.3 oz.
The z-score corresponding to the 2.3% percentile is approximately -1.81.
Then, you can use the formula:
z = (x - μ) / σ
where x is the weight you want to find, μ is the mean weight (12 oz), and σ is the standard deviation (which is the square root of the variance = 0.4 oz).
Plugging in the values:
-1.81 = (x - 12) / 0.4
Solving for x:
x = -1.81 * 0.4 + 12 = 11.276
Rounding to one decimal place, the weight that will be exceeded by 2.3% of the packages is 11.3 oz.
9 answers