The table below summarises the calculation for the standard deviation of x-bar.
![\begin{tabular} {|c|c|c|c|} Drawing (x)&$\bar{x}$&$x-\bar{x}$&$(x-\bar{x})^2\\[1ex] 2,2,2&2&-2.5&6.25\\ 2,2,3&2.3&-2.2&4.84\\ 2,2,5&3&-1.5&2.25\\ 2,2,8&4&-0.5&0.25\\ 2,3,3&2.7&-1.8&3.24\\ 2,3,5&3.3&-1.2&1.44\\ 2,3,8&4.3&-0.2&0.04\\ 2,5,5&4&-0.5&0.25\\ 2,5,8&5&0.5&0.25\\ 2,8,8&6&1.5&2.25\\ 3,3,3&3&-1.5&2.25\\ 3,3,5&3.7&-0.8&0.64\\ 3,3,8&4.7&0.2&0.04\\ 3,5,5&4.3&-0.2&0.04\\ 3,5,8&5.3&0.8&0.64\\ 3,8,8&6.3&1.8&3.24\\ 5,5,5&5&0.5&0.25\\ 5,5,8&6&1.5&2.25\\ 5,8,8&7&2.5&6.25\\ 8,8,8&8&3.5&12.25\\ \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7Cc%7Cc%7C%7D%0ADrawing%20%28x%29%26%24%5Cbar%7Bx%7D%24%26%24x-%5Cbar%7Bx%7D%24%26%24%28x-%5Cbar%7Bx%7D%29%5E2%5C%5C%5B1ex%5D%0A2%2C2%2C2%262%26-2.5%266.25%5C%5C%0A2%2C2%2C3%262.3%26-2.2%264.84%5C%5C%0A2%2C2%2C5%263%26-1.5%262.25%5C%5C%0A2%2C2%2C8%264%26-0.5%260.25%5C%5C%0A2%2C3%2C3%262.7%26-1.8%263.24%5C%5C%0A2%2C3%2C5%263.3%26-1.2%261.44%5C%5C%0A2%2C3%2C8%264.3%26-0.2%260.04%5C%5C%0A2%2C5%2C5%264%26-0.5%260.25%5C%5C%0A2%2C5%2C8%265%260.5%260.25%5C%5C%0A2%2C8%2C8%266%261.5%262.25%5C%5C%0A3%2C3%2C3%263%26-1.5%262.25%5C%5C%0A3%2C3%2C5%263.7%26-0.8%260.64%5C%5C%0A3%2C3%2C8%264.7%260.2%260.04%5C%5C%0A3%2C5%2C5%264.3%26-0.2%260.04%5C%5C%0A3%2C5%2C8%265.3%260.8%260.64%5C%5C%0A3%2C8%2C8%266.3%261.8%263.24%5C%5C%0A5%2C5%2C5%265%260.5%260.25%5C%5C%0A5%2C5%2C8%266%261.5%262.25%5C%5C%0A5%2C8%2C8%267%262.5%266.25%5C%5C%0A8%2C8%2C8%268%263.5%2612.25%5C%5C%0A%5Cend%7Btabular%7D)
Therefore, the standard deviation of x-bar is approximately 1.23.
Therefore, the standard deviation of x-bar is approximately 1.23.
Match the number (1-5) of each coordinate pair with the corresponding letter of the point from the graph.
2 answers:
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Given Information:
John's mean monthly commission = μ = $10,000
Standard deviation of monthly commission = σ = $2,000
Answer:
The probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
We want to find out the probability that John's commission from the jewelry store is between $9,000 and $11,000?
The z-score corresponding to 0.50 is 0.6915
The z-score corresponding to -0.50 is 0.3085
Therefore, the probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.4, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.50 then go for 0.00 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.