Assume that each month the average Canadian household generates an average of 13kg of newspaper for garbage or recycling with a standard deviation of 1kg. What is the probability that a randomly selected household generates between 12 and 15 kg of newspaper per month?

Question

Assume that each month the average Canadian household generates an average of 13kg of newspaper for garbage or recycling with a standard deviation of 1kg. What is the probability that a randomly selected household generates between 12 and 15 kg of newspaper per month?

A) 23.08%
b) 34.13%
c) 47.72%
d) 49.87%
e) 81.85%

By using z-scores I managed the answer of 49.87. Somehow it appears that other classmates consistently attained 81.85, how is this so?

Answer 1

http://davidmlane.com/hyperstat/z_table.html

Your classmates are right.

Answer 2

However, on an exam I will not have a computed normal distributions.

How do you manage this manually?

Answer 3

Never-mind. Question answered.Thank you.

Answer 4

To solve this problem using z-scores, you need to standardize the values of 12kg and 15kg to calculate the area under the normal distribution curve.

The formula for calculating a z-score is as follows:
z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

Let's calculate the z-scores for 12kg and 15kg, assuming the mean (μ) is 13kg and the standard deviation (σ) is 1kg:

For 12kg:
z1 = (12 - 13) / 1 = -1

For 15kg:
z2 = (15 - 13) / 1 = 2

Now, we need to find the probability of a randomly selected household generating between 12kg and 15kg of newspaper per month. This corresponds to finding the area under the standard normal distribution curve between z1 and z2.

To look up these values in the standard normal distribution table, you can calculate the cumulative probability from the z-scores:

P(z1 < Z < z2) = P(Z < z2) - P(Z < z1)

Using the z-table, the cumulative probability for z2 (2) is approximately 0.9772, and for z1 (-1) is approximately 0.1587.

Therefore, the probability that a randomly selected household generates between 12kg and 15kg of newspaper per month is:

P(-1 < Z < 2) = P(Z < 2) - P(Z < -1) = 0.9772 - 0.1587 = 0.8185 or 81.85%.

So, the correct answer is e) 81.85%. If your classmates consistently attained this answer while using z-scores, it is possible that they made an error in their calculations or looked up the incorrect values in the z-table.