Asked by Amrita Nijjer on Jun 12, 2024
Verified
At a furniture factory,tables must be assembled,finished,and packaged before they can be shipped to stores.Based on past experience,the manager finds that the means and standard deviations (in minutes) of the times for each phase are as shown in the table: Phase Mean SD Assembly 25.42.6 Finishing 35.53.6 Packaging 14.61.8\begin{array} { l | l | l } \text { Phase } & \text { Mean } & \text { SD } \\\hline \text { Assembly } & 25.4 & 2.6 \\\text { Finishing } & 35.5 & 3.6 \\\text { Packaging } & 14.6 & 1.8\end{array} Phase Assembly Finishing Packaging Mean 25.435.514.6 SD 2.63.61.8 What are the mean and standard deviation of the total time to prepare a table for shipping? Assume that the times for each phase are independent.
A) ? = 46.03 min,? = 4.79 min
B) ? = 75.5 min,? = 22.96 min
C) ? = 75.5 min,? = 4.79 min
D) ? = 46.03 min,? = 8 min
E) ? = 75.5 min,? = 8 min
Standard Deviation
A measure of the amount of variation or dispersion of a set of values, indicating how much the values differ from the mean of the set.
Furniture Factory
A manufacturing site where raw materials are processed and assembled into furniture for use and sale.
Assembly
The process of putting together individual pieces to create a complete product or compiling and linking program code into a usable software program.
- Attain a comprehensive understanding of mean and standard deviation in the context of probability and statistics.
- Evaluate the variance and standard deviation for merged independent variables.
Verified Answer
NA
Nyeika ArcherJun 18, 2024
Final Answer :
C
Explanation :
The mean total time is the sum of the individual means: 25.4 + 35.5 + 14.6 = 75.5 minutes. The standard deviation of the total time, assuming independence, is the square root of the sum of the squares of the individual standard deviations: sqrt((2.6)^2 + (3.6)^2 + (1.8)^2) = sqrt(6.76 + 12.96 + 3.24) = sqrt(22.96) = 4.79 minutes.
Learning Objectives
- Attain a comprehensive understanding of mean and standard deviation in the context of probability and statistics.
- Evaluate the variance and standard deviation for merged independent variables.