Question 153265This question is from textbook
: Trevor wants to buy a local restaurant. 60% of the business days it's open, the restaurant makes a $850 profit. Estimate the probability that the store will make p$850 profit more than 17 out of the next 20 business days. If this actually happened, might you suspect that p is greater than 0.60?
High school seniors in SAT math had a mean score of 500 with a standard deviation 100. In an ACT, the mean was 18 and a standard deviation of 6. Both scores are normally distributed.
a) An engineering school only accepts SAT and ACT scores in the top 10%. What's the minimum SAT and ACT scores for this program
b) Suppose the school accepts SAT and ACT scores in the top 20%. What are the minimum SAT and ACT scores for this program?
c) IF the school accepts the top 60% scores, what are the minimum SAT and ACT scores?
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Trevor wants to buy a local restaurant. 60% of the business days it's open, the restaurant makes a $850 profit. Estimate the probability that the store will make p$850 profit more than 17 out of the next 20 business days. If this actually happened, might you suspect that p is greater than 0.60?
Comment: Your problem does not make sense as posted.
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High school seniors in SAT math had a mean score of 500 with a standard deviation 100. In an ACT, the mean was 18 and a standard deviation of 6. Both scores are normally distributed.
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a) An engineering school only accepts SAT and ACT scores in the top 10%. What's the minimum SAT and ACT scores for this program
Find the z-score that separates the top 10% of the standard normal curve
area from the bottom 90%:
That value is 1.2816
Now find the raw ACT and SAT scores that correspond using z=(x-u)/sigma.
ACT: 1.2816 = (x-18)/6; x = 6*1.2816+18 = 25.689..
SAT: 1.2816 = (x-500)/100; x = 100*1.2816+500 = 628.16
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b) Suppose the school accepts SAT and ACT scores in the top 20%. What are the minimum SAT and ACT scores for this program?
Follow the same procedure with z = 0.8416
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c) IF the school accepts the top 60% scores, what are the minimum SAT and ACT scores?
Follow the same procedure with z = -0.2533
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Chers,
Stan H.
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