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Math Homework# Assume That The Weight Loss For The First Month Of A Diet Program

1.Question :Assume that the weight...

1.Question :Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost.

Less than 11 pounds

Student Answer:

1/3

1/6

5/6

5/7

2.Question :If z is a standard normal variable, find the probability.

The probability that z is less than 1.13

Student Answer:

0.1292

0.8708

0.8485

0.8907

3.Question :Solve the problem. Round to the nearest tenth unless indicated otherwise.

The amount of rainfall in January in a certain city is normally distributed with a mean of 4.3 inches and a standard deviation of 0.3 inches. Find the value of the quartile .

Student Answer:

1.1

4.1

4.2

4.5

4.Question :Assume that X has a normal distribution, and find the indicated probability.

The mean is 15.2 and the standard deviation is 0.9. Find the probability that X is greater than 17.

Student Answer:

0.9713

0.9821

0.0228

0.9772

5.Question :Solve the problem.

The weights of the fish in a certain lake are normally distributed with a mean of 19 lb and a standard deviation of 6. If 4 fish are randomly selected, what is the probability that the mean weight will be between 16.6 and 22.6 lb?

Student Answer:

0.0968

0.4032

0.6730

0.3270

6.Question :Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.

A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, estimate the probability of getting at least 20% correct.

Student Answer:

0.0901

0.8508

0.3508

0.1492

7.Question :Use the normal distribution to approximate the desired probability.

Find the probability that in 200 tosses of a fair die, we will obtain at least 40 fives.

Student Answer:

0.0871

0.1210

0.2229

0.3871

8.Question :Solve the problem.

The following confidence interval is obtained for a population proportion, p: (0.707, 0.745). Use these confidence interval limits to find the margin of error, E.

Student Answer:

0.038

0.017

0.019

0.020

9.Question :Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places.

95% confidence; the sample size is 10,000, of which 40% are successes

Student Answer:

0.0072

0.0110

0.0126

0.0096

10.Question :Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

n = 110, x = 55; 88% confidence

Student Answer:

0.425 < p < 0.575

0.421 < p < 0.579

0.422 < p < 0.578

0.426 < p < 0.574

11.Question :Use the given data to find the minimum sample size required to estimate the population proportion.

Margin of error: 0.05; confidence level: 99%; from a prior study, is estimated by 0.15.

Student Answer:

17

339

407

196

12. Question: Solve the problem. Round the point estimate to the nearest thousandth.

430 randomly selected light bulbs were tested in a laboratory, 224 lasted more than 500 hours. Find a point estimate of the proportion of all light bulbs that last more than 500 hours.

Student Answer:

0.521

0.519

0.479

0.343

13. Question: Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

When 319 college students are randomly selected and surveyed, it is found that 120 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.

Student Answer:

0.313 < p < 0.439

0.332 < p < 0.421

0.323 < p < 0.429

0.306 < p < 0.446

14. Question: Solve the problem.

In a certain population, body weights are normally distributed with a mean of 152 pounds and a standard deviation of 26 pounds. How many people must be surveyed if we want to estimate the percentage who weigh more than 180 pounds? Assume that we want 96% confidence that the error is no more than 4 percentage points.

Student Answer:

657

317

501

232

15. Question: Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted.

College students' annual earnings: 99% confidence; n = 76,

Student Answer:

$196

$891

$233

$258

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