Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Answer:
0.0901 = 9.01% of packages will incur such a charge
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Sum of normal variables:
When we add normal variables, the mean will be the sum of the means, while the standard deviation is the square root of the sum of the variances.
Centerpieces are normally distributed with mean of 30 ounces and standard deviation of 2 ounces.
This means that [tex]\mu_C = 30, \sigma_C = 2[/tex]
The weights of the shipping boxes are normally distributed with mean of 12 ounces and standard deviation of 1 ounce.
This means that [tex]\mu_S = 12, \sigma_S = 1[/tex]
Suppose that centerpieces are chosen at random and packed into randomly chosen shipping boxes.
The shipment is given by the centerpice plus the shipping box. So the mean and the standard deviation of the weight are given by:
[tex]\mu = \mu_C + \mu_S = 30 + 12 = 42[/tex]
[tex]\sigma = \sqrt{\sigma_C^2 + \sigma_S^2} = \sqrt{2^2 + 1^2} = \sqrt{5} = 2.236[/tex]
If a package exceeds 45 ounces, an additional charge is incurred. What is the proportion of packages will incur such a charge
This proportion is 1 subtracted by the pvalue of Z when X = 45. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{45 - 42}{2.236}[/tex]
[tex]Z = 1.34[/tex]
[tex]Z = 1.34[/tex] has a pvalue of 0.9099
1 - 0.9099 = 0.0901
0.0901 = 9.01% of packages will incur such a charge
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
