A prototype automotive tire has a design life of 38,500 miles with a standard deviation of 2,500 miles. The manufacturer tests 60 such tires. On the assumption that the actual population mean is 38,500 miles and the actual population standard deviation is 2,500 miles, find the probability that the sample mean will be less than 36,000 miles. Assume that the distribution of lifetimes of such tires is normal.   (a) Let X = number of miles on a single tire. Write the question above in terms of this variable X.       (b) Using the software tool above, find the probability stated on part (a)            (c) Using the software tool above, graph the probability of stated on part (b)

A​ person's body mass index​ (BMI) is computed by dividing the weight​ (kg) by the square of height​ (m). The accompanying table contains the BMI statistics for random samples of males and females. Assume that the two samples are independent simple random samples selected from normally distributed​populations, and do not assume that the population standard deviations are equal. Let population 1 be females.   Female​ BMI: n=69 x=29.14 s=7.41 Male​ BMI: n=79 x=28.18 s=5.24   The test statistic is   The​ P-value is     Construct a confidence interval appropriate for testing the claim in part​ (a).   The ___​% confidence interval estimate is ___<μ1−μ2<___.

A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At a = 0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient Total Blood Cholesterol (Before) Total Blood Cholesterol (After) OA. Ho Hd #0 HA Hd=0 OC. Ho Hd ≤0 HA Hd >0 Calculate the standardized test statistic t= (Round to three decimal places as needed.) Calculate the P-value P-value= (Round to four decimal places as needed) State the conclusion. 1 205 204 Ho. There C 2 225 222 Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be…

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -0.71°C.

Assume that weights of adult females are normally distributed with a mean of 77 kg and a standard deviation of 22 kg. What percentage of individual adult females have weights between 71 kg and 83 ​kg? If samples of 100 adult females are randomly selected and the mean weight is computed for each​ sample, what percentage of the sample means are between 71 kg and 83 ​kg?