Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 500 and a standard deviation of 100. Find the probability that a student will score

1. (a)over 650.
2. (b)less than 459.
3. (c)between 325 and 675.

Answer :

Answer :

Answer :

1. (d)If a school only admits students who score over 680, what proportion of the students pool would be eligible for admission?
2. Answer :
3. (e)What limit (score) would you set that makes the top 20% of the students eligible? (Choose closest number in table. Do not interpolate).
4. Answer :
5. (f)If 16 examinations are selected at random and their mean is calculated,
6. what is the expected average score? Answer :
7. what is the standard deviation for the average score? Answer :

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1. is the distribution of the average score exactly or approximately normal? Explain.
2. The distribution of the average score is (circle one) normally distributed.
3. Because :
4. What is the probability that the average score of the 16 examinations is over 650?
5. Answer :

2. Patients with chronic kidney failure may be treated by dialysis, using a machine that removes toxic wastes from the blood, a function normally performed by the kidneys. Kidney failure and dialysis can cause other changes, such as retention of phosphorus, that must be corrected by changes in diet. A study of the nutrition of dialysis patients measured the level of phosphorus in the blood of 45 dialysis patients and their average phosphorus level was 5.2 mg/dl.

1. (a)Assuming blood phosphorus varies according to a normal distribution, with p = 0.9 mg/dl, find a 99% confidence interval for the mean blood phosphorus level for dialysis patients.
2. 99% CI :
3. (b)What is the margin of error in the 99% confidence interval found in part (a)
4. Margin of error :
5. (c)Interpret the confidence interval found in part (a) Interpretation:
6. (d)If the level of confidence is changed to 90%, and all the other parameters stay the same, what effect would lowering the level of confidence have in the size of the confidence interval? Explain.

exactly / approximately

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The 90% confidence interval is (circle one) than the 99% confidence interval.

Because:

(e) How many dialysis patients should be sampled to obtain a margin of error of no more than 0.3 in a 99% confidence interval?

Sample size =

3. Environmental Science & Technology (1993) reported on a study of contaminated soil in The Netherlands. Seventy-two 400-grams soil specimens were sampled, dried, and analyzed for the contaminant cyanide. The cyanide concentration (in mg/kg) of each soil specimen was determined using an infrared microscopic method. The sample resulted in a mean cyanide level of 84 mg/kg. Assume p = 80 mg/kg. Test the hypothesis that the true mean cyanide level in soil in The Netherlands does not exceed 100 mg/kg. Use a significance level of 0.01.

1. (a)State the null and alternative hypotheses
2. H0 : Ha :
3. (b)Calculate the value of the test statistic. Show workings.
4. Value of test statistic =
5. (c)Find the critical value(s) and draw the acceptance and rejection region.

wider / narrower / the same

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(d) Decision is:

Conclusion:

(e) Calculatethep-valueassociatedwiththistest.

P-value =

(f) Decision based on the p-value of the test

(Circle One) :

(Circle One) :

Reject H0 / Not Reject H0

Reason for decision :