# Assignment #3

Question 1 Question 1 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  1/3  1/6  5/6  5/7Question 2 If z is a standard normal variable, find the probability. The probability that z is less than 1.13  0.1292  0.8708  0.8485  0.8907Question 3 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 Q1.  1.1  4.1  4.2  4.5
Question 4 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.  0.9713  0.9821  0.0228  0.9772
Question 5 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?  0.0968  0.4032  0.6730  0.3270Question 6 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.  0.0901  0.8508  0.3508  0.1492

Question 7 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.  0.0871  0.1210  0.2229  0.3871Question 8 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.  0.038  0.017  0.019  0.020Question 9 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  0.0072  0.0110  0.0126  0.0096Question 10 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  0.425 < p < 0.575  0.421 < p < 0.579  0.422 < p < 0.578  0.426 < p < 0.574Question 11 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, ^p is estimated by 0.15.  17  339  407  196Question 12 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.  0.521  0.519  0.479  0.343Question 13 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.  0.313 < p < 0.439  0.332 < p < 0.421  0.323 < p < 0.429  0.306 < p < 0.446Question 14 Solve the problem. In a certain population, body weights are normally distributed.  Not knowing the sample mean or standard deviation, how many people must be surveyed?  Assume that we want 96% confidence that the error is no more than 4 percentage points.  660  317  501  232Question 15 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,    \$196  \$891  \$233  \$258Question 16 Use the confidence level and sample data to find a confidence interval for estimating the population mu. Round your answer to the same number of decimal places as the sample mean. A random sample of 105 light bulbs had a mean life of 441 hours with a standard deviation of 40 hours. Construct a 90% confidence interval for the mean life, mu, of all light bulbs of this type.  433 hr < mu < 449 hr  435 hr < mu < 447 hr  431 hr < mu < 451 hr  432 hr < mu < 450 hrQuestion 17 Use the given information to find the minimum sample size required to estimate an unknown population mean mu. How many women must be randomly selected to estimate the mean weight of women in one age group. We want 90% confidence that the sample mean is within 3.7 lb of the population mean, and the population standard deviation is known to be 28 lb.  221  156  153  155Question 18 Assume that a sample is used to estimate a population mean mu. Use the given confidence level and sample data to find the margin of error. Assume that the sample is a simple random sample and the population has a normal distribution. Round your answer to one more decimal place than the sample standard deviation. 95% confidence; n = 21; x-bar = 0.16; s = 0.16  0.085  0.068  0.063  0.073Question 19 Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu. Assume that the population has a normal distribution. Thirty randomly selected students took the calculus final. If the sample mean was 83 and the standard deviation was 13.5, construct a 99% confidence interval for the mean score of all students.  76.21 < mu < 89.79  76.23 < mu < 89.77  76.93 < mu < 89.07  78.81 < mu < 87.19Question 20 Solve the problem.Find the critical value XL2 corresponding to a sample size of 24 and a confidence level of 95 percent.  35.172  13.091  11.689  38.076

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