Question

Using the answers from the table above, answer ALL of the questions below. For questions 1 - 13, draw a normal curve and indicate the area that you are calculating the probability of. For questions 14 – 22, use the appropriate formulas and show all of your calculations.

Be sure to turn in the table above along with your answers to all of the questions below. Place your answers in a folder with your name clearly written at the top of the folder.

1. If one student is randomly selected from the USA born group, find the probability of getting someone with a GPA greater than 3.88.

2. If one student is randomly selected from the Non-USA born group, find the probability of getting someone with a GPA greater than 3.88.

3. If one student is randomly selected from the USA born group, find the probability of getting someone between the ages of 20 and 25.

4. If 9 students are randomly selected from the Non-USA born group, find the probability that their mean age is between 22 and 37.

5. If 25 students are randomly selected from the USA born group, find the probability that their mean GPA is between 2.50 and 3.50.

6. Calculate the age of students at the 90^th percentile for the USA born group.

7. Calculate the age of student at the 90^th percentile for the Non-USA born group.

8. Assume that Broward College has announced that it will give a scholarship to students born in the USA who have a GPA between 3.75 and 4.00; calculate the percentage of US born students who will be eligible for a scholarship.

9. Assume that Broward College has announced that it will give a scholarship to foreign-born students who have a GPA between 3.75 and 4.00; calculate the percentage of foreign-born students who will be eligible for a scholarship.

10. Assume that Broward College has announced that it will give scholarships to students who have GPA’s that falls within the top 2% of all GPA’s. Calculate the GPA a student will need to earn a scholarship from the USA born group.

11. Assume that Broward College has announced that it will give scholarships to students who have GPA’s that falls within the top 2% of all GPA’s. Calculate the GPA a student will need to earn a scholarship from the foreign-born born group.

12. To encourage students to spend more time doing homework at home, Broward College has announced that it will give a $100 scholarship to students who spend more than 10 hours per week doing homework at home. Calculate the percentage of students who will receive the scholarship from the USA born group.

13. In order to encourage students to spend more time doing homework at home, Broward College has announced that it will give a $100 scholarship to students who spend more than 10 hours per week doing homework at home. Calculate the percentage of students who will receive the scholarship from the foreign-born group.

14. In a survey of 735 students at Broward College North Campus, results revealed that 283 students were born outside of the USA. Construct a 97% confidence interval estimate for the proportion of students who were born outside the USA. Give your interpretation of the confidence interval estimate.

15. In a survey of 735 students at Broward College North Campus, results revealed that the mean GPA for US born students was 3.09, with a standard deviation of .51. Construct a 98% confidence interval estimate for the mean GPA of US born students. Give your interpretation of the confidence interval estimate.

16. In a survey of 283 foreign-born students at North Campus, the mean hours spent on homework was 11.79, with a standard deviation of 7.15. Construct a 95% confidence interval estimate for the mean hours spent on homework for foreign-born students. Give your interpretation of the confidence interval estimate.

17. Suppose you wanted to estimate the percentage of students at North Campus who are foreign born, how many students must you survey if you wanted to be 95% confident in your result, with a margin of error of no more than 4%. Assume you have no estimate of the percentage of students who are foreign-born.

18. Suppose you wanted to estimate the percentage of native-born students at North Campus, how many students must you survey if you wanted to be 90% confident in your result, with a margin of error of no more than 2%. Assume you have an estimate of native-born students at North Campus which is equal to 65%.

19. Suppose you wanted to estimate the mean age of native-born students at North Campus. How many students must you survey if you wanted to be 99% confident in your result and your error is no more than 2 years? Use the standard deviation of 8.65.

20. In a survey of 735 students at Broward College, North Campus, results revealed that 283 students were foreign-born and 452 were native-born. Using these results, conduct a hypothesis test to test the claim, at the .03 significance level, that the proportion of students who are born outside of the USA is greater than 35 percent. Be sure to show all the steps in the hypothesis testing procedure including the null and alternative hypotheses, the calculation of the test statistic, and correct wording of the final conclusion.

21. In a survey of 735 students at Broward College, North Campus, the mean GPA was found to be 3.02 with a standard deviation of .42. Using these results, test the claim at the .05 significance level that the mean GPA of students at North Campus is equal to 3.00. Be sure to show all the steps in the hypothesis testing procedure including the null and alternative hypotheses, the calculation of the test statistic, and correct wording of the final conclusion.

22. In a survey of 735 students at Broward College, North Campus, the mean number of hours spent on homework was 7.15 with a standard deviation of 3.20. Using these results, test the claim at the .05 significance level that the mean number of hours spent on homework by students at North Campus is equal to 8.50. Be sure to show all the steps in the hypothesis testing procedure including the null and alternative hypotheses, the calculation of the test statistic, and correct wording of the final conclusion.

KX Data 2 us.dsx Student ID Total Credit Hours GPA Hours Spent on school work at hon 3.5 3.2 3.2 3.7 3.7 173 182 193 204 211 212 224 227 256 265 291 292 298 303 319 324 342 347 350 352 357 367 371 376 389 19 27 19 42 32 15 12 76 10 20 20 9 19 27 10 27 12 13 14 15 24 12 24 15 37 54 20 3.6 10 30 25 25 10 12 10 12 17 57 36 26 19 19 21 26 28 20 46 25 16 24 25 23 25 37 20 23 412 416 419 434 2.9 20 25 30 19 31 3.2 12 Data Outside us.xlsx Student ID Total Credit Hours GPA Hours spent on school work at ho 45 28 18 20 23 13 2.5 10 29 35 37 20 28 53 2.5 19 30 25 15 16 9 10 18 29 23 24 17 65 70 73 100 12 13 37 30 12 21 25 26 26 60 70 24 23 121 132 28 24 20 24 45 45 133 35 37 20 19 12 135 39 138 139 140 150 152 154 156 160 3.2 56 24 15 24 56 24 34 16 23 3.2 30 28 27 34 21 15 161 163 167 170 3.7 13 3.5 21 24 63 42 38 15 12 Studenks born Stsens n in the U.SOutside USA Mean GPA: 30G 23.57 Mn Houk spent 1.13.4 3.13 0.53f 29.2 Stomard Deviahon .206.157 Man Age 2 20.53 l6.13 Shárdard Deviatien 16.5l

Answer 1

Solution: Obtain the probability Let X be the random variable. Thus, the required probability is, X-3.06 3.88-3.06 P(x>3.88)-P0.4980.498 - P(Z >1.6466) -0.0498 Distribution Plot Normal Mean d, StDe 0.3 0.2 Obtain the probability Let X be the random variable. Thus, the required probability is,

8 053413) X-3.13 3.88-3.13 0.534 0.534 P(X>3.88)-P - P(Z >1.4045) 00801 Distribution Plot Normal, Mean-, StDev 0.4 0.3 .08009 0.0 Obtain the probability. Let X be the random variable. Thus, the required probability is, P( 20 < X < 25)-P( ) 20-2357 Y-23.57 25-23.57 < 6.280 , 6.280 6.280 -P(-0.5685< Z <0.2277) 0.3052

Distribution Plot 5685 822 4 Obtain the probability Let X be the random variable. Thus, the required probability is, 22-29.2.X-29.2 , 37-29.2 10.157 (10.157 10.157 P(22 < X <37- P(-2.1266<Z<2.3038) -0.9727

Distribution Plot Normal, Mean , StDev 0.4 03 .1266