I need help solving theses problems, it is time sensitive as i need them done by noon tomorrow. It is really important that the work be shown and the answers come with justification..

1. Assume the weights of men are normally distributed with a mean of 170 lbs and a standard deviation of 30 lbs. Show all work. Just the answer, without supporting work, will receive no credit. (a) (b) Find the 75th percentile for the distribution of men's weights. What is the probability that a randomly selected man weighs more than 200 lbs 2. (a) (b) Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500 and a standard deviation of 100. Show all work. Just the answer, without supporting work, will receive no credit. If a random sample of 64 test scores is selected, what is the standard deviation of the sample mean? What is the probability that 64 randomly selected test scores will have a mean test score that is between 475 and 525? 3. A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a 90% confidence interval estimate of the proportion of adults believing in global warming. Show all work. Just the answer, without supporting work, will receive no credit. 4. In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults were treated with garlic tablets. Cholesterol levels were measured before and after the treatment. The changes in their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 14. Construct a 95% confidence interval estimate of the mean change in LDL cholesterol after the garlic tablet treatment. Show all work. Just the answer, without supporting work, will receive no credit. 5. Mimi is interested in testing the claim that banana is the favorite fruit for more than 50% of the adults. She conducted a survey on a random sample of 100 adults. 58 adults in the sample chose banana as his / her favorite fruit. Assume Mimi wants to use a 0.10 significance level to test the claim. (a) Identify the null hypothesis and the alternative hypothesis. (b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. Is there sufficient evidence to support the claim that banana is the favorite fruit for more than 50% of the adults? Explain. (c) (d) 6. In a study of freshman weight gain, the measured weights of 5 randomly selected college students in September and April of their freshman year are shown in the following table. Student 1 2 3 4 5 Weight (kg) September April 67 66 53 55 64 68 71 70 70 75 Is there evidence to suggest that the mean weight of the freshmen in April is greater than the mean weight in September? Assume we want to use a 0.10 significance level to test the claim. (a) Identify the null hypothesis and the alternative hypothesis. (b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. Is there sufficient evidence to support the claim that the mean weight of the freshmen in April is greater than the mean weight in September? Justify your conclusion. (c) (d) 7. In a pulse rate research, a simple random sample of 40 men results in a mean of 80 beats per minute, and a standard deviation of 11.3 beats per minute. Based on the sample results, the researcher concludes that the pulse rates of men have a standard deviation greater than 10 beats per minutes. Use a 0.05 significance level to test the researcher's claim. (a) Identify the null hypothesis and alternative hypothesis. (b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. Is there sufficient evidence to support the researcher's claim? Explain. (c) (d) 8. The UMUC Daily News reported that the color distribution for plain MM's was: 40% brown, 20% yellow, 10% orange, 10% green, and 20% tan. Each piece of candy in a random sample of 100 plain MM's was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct. Show all work and justify your answer. Color Number Brown 42 Yellow 21 Orange 12 Green 7 Tan 18 (a) Identify the null hypothesis and the alternative hypothesis. (b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. (c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit. (d) Is there sufficient evidence to support the claim that the published color distribution is correct? Justify your answer. 9. A STAT 200 instructor believes that the average quiz score is a good predictor of final exam score. A random sample of 5 students produced the following data where x is the average quiz score and y is the final exam score. x y (a) (b) 80 145 50 150 60 130 100 180 70 120 Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit. Based on the equation from part (a), what is the predicted final exam score if the average quiz score is 90? Show all work and justify your