Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability between those two Z scores.
If you pick one fruit at random, what is the probability that it will weigh between 334 grams and 344 grams?
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability between those two Z scores.
Step 1: Calculate the z-score for the lower bound of the range.
z = (x - μ) / σ
where x is the lower bound, μ is the mean, and σ is the standard deviation.
For the lower bound of 334 grams:
z = (334 - 353) / 6
Step 2: Calculate the z-score for the upper bound of the range.
For the upper bound of 344 grams:
z = (344 - 353) / 6
Step 3: Look up the cumulative probability from the z-table for both z-scores.
The table gives the cumulative probability up until a particular z-score.
For the lower bound of 334 grams:
P(z < -3.29) ≈ 0.0005 (using a z-table)
For the upper bound of 344 grams:
P(z < -1.5) ≈ 0.0668 (using a z-table)
Step 4: Calculate the probability between the two z-scores.
P(334 < x < 344) ≈ P(z < -1.5) - P(z < -3.29)
≈ 0.0668 - 0.0005
≈ 0.0663 or 6.63%
Therefore, the probability that a randomly picked fruit weighs between 334 grams and 344 grams is approximately 6.63%.
First, let's convert the weights to z-scores using the formula:
z = (x - μ) / σ
where z is the z-score, x is the weight of the fruit, μ is the mean weight, and σ is the standard deviation.
For the lower limit of 334 grams:
z = (334 - 353) / 6 = -3.17
For the upper limit of 344 grams:
z = (344 - 353) / 6 = -1.5
Once we have the z-scores, we can find the corresponding probabilities using a standard normal distribution table or a statistical software.
The probability of a fruit weighing between 334 grams and 344 grams is equal to the area under the normal curve between the z-scores -3.17 and -1.5.
Using a standard normal distribution table, we can find the probabilities corresponding to these z-scores:
P(Z < -1.5) = 0.0668 (from the table)
P(Z < -3.17) ≈ 0 (since it's beyond the lower limit of the table)
To find the probability between the two z-scores, we subtract the probabilities:
P(-1.5 < Z < -3.17) = P(Z < -1.5) - P(Z < -3.17) ≈ 0.0668 - 0 = 0.0668
Therefore, the probability that a randomly picked fruit will weigh between 334 grams and 344 grams is approximately 0.0668 or 6.68%.