Question 878456: I'm having a hard time understanding how to compute this question. I'm just starting my summer school class and my teacher is absolutely HORRID! It's his first time ever teaching and he doesn't speak english well!
My question is how do I solve this question?
Question:
SunBlush Technologies tracks their daily profits and has found that the distribution of profits is approximately normal with a mean of $21,900.00 and a standard deviation of about $500.00. Using this information, answer the following questions. Round your intermediate answers (z-values) to 2 decimal places in order to be able to read the corresponding area values from the table.
For full marks your answer should be accurate to at least four decimal places.
Compute the probability that tomorrow's profit will be:
a) between $20,580.00 and $21,405.00
b) less than $22,615.00 or greater than $23,085.00
c) less than $22,455.00
d) between $20,525.00 and $22,785.00
e) between $22,825.00 and $23,335.00
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! For this entire problem, I'm using this table
a)
Compute the z-score when the raw score is x = 20580
z = (x - mu)/sigma
z = (20580 - 21900)/500
z = -2.64
Use the table (mentioned above) to find that the area to the left of z = -2.64 is 0.0041
Compute the z-score when the raw score is x = 21405
z = (x - mu)/sigma
z = (21405 - 21900)/500
z = -0.99
Use the table to find that the area to the left of z = -0.99 is 0.1611
Subtract the two areas: 0.1611 - 0.0041 = 0.1570
The area between z = -2.64 and z = -0.99 is 0.1570
The area between x = 20580 and x = 21405 is 0.1570
The two areas are the same because we applied a z-score transform.
That means the probability of being between $20,580.00 and $21,405.00 is 0.1570
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b)
Compute the z-score when the raw score is x = 22615
z = (x - mu)/sigma
z = (22615 - 21900)/500
z = 1.43
Use the table to find that the area to the left of z = 1.43 is 0.9236
Compute the z-score when the raw score is x = 23085
z = (x - mu)/sigma
z = (23085 - 21900)/500
z = 2.37
Use the table to find that the area to the left of z = 2.37 is 0.9911
Subtract that from 1 to get 1-0.9911 = 0.0089
The area to the right of z = 2.37 is 0.0089
Add the two areas: 0.9236+0.0089 = 0.9325
Final Answer: 0.9325
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c)
Compute the z-score when the raw score is x = 22455
z = (x - mu)/sigma
z = (22455 - 21900)/500
z = 1.11
Use the table to find that the area to the left of z = 1.11 is 0.8665
Final Answer: 0.8665
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d)
Compute the z-score when the raw score is x = 20525
z = (x - mu)/sigma
z = (20525 - 21900)/500
z = -2.75
Use the table (mentioned above) to find that the area to the left of z = -2.75 is 0.0030
Compute the z-score when the raw score is x = 22785
z = (x - mu)/sigma
z = (22785 - 21900)/500
z = 1.77
Use the table to find that the area to the left of z = 1.77 is 0.9616
Subtract the two areas: 0.9616 - 0.0030 = 0.9586
Final Answer: 0.9586
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e)
Compute the z-score when the raw score is x = 22825
z = (x - mu)/sigma
z = (22825 - 21900)/500
z = 1.85
Use the table (mentioned above) to find that the area to the left of z = 1.85 is 0.9678
Compute the z-score when the raw score is x = 23335
z = (x - mu)/sigma
z = (23335 - 21900)/500
z = 2.87
Use the table to find that the area to the left of z = 2.87 is 0.9979
Subtract the two areas: 0.9979 - 0.9678 = 0.0301
Final Answer: 0.0301
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