Given the discrete uniform population shown to the right, find the probability that a random sample of size 96, selected with replacement, will yield a sample mean greater than 10.4 but less than 11.2. Assume the means are measured to the nearest tenth. f(x) = {1/3, x = 2, 10, 18 0, elsewhere Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The probability is . (Round to four decimal places as needed.)
A random sample of size 49 is taken from a normal population having a mean of 70 and a standard deviation of 7. A second random sample of size 25 is taken from a different normal population having a mean of 60 and a standard deviation of 6. Find the probability that the sample mean computed from the 49 measurements will exceed the sample mean computed from the 25 measurements by at least 7.9 but less than 10.9. Assume the difference of the means to be measured to the nearest tenth. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard nomal distribution table. The probability is (Round to four decimal places as needed.)
The mean score for freshmen on an aptitude test at a certain college is 530, with a standard deviation of 70. Assume the means to be measured to any degree of accuracy. What is the probability that two groups selected at random, consisting of 45 and 70 students, respectively, will differ in their mean scores by (a) more than 16 points? (b) an amount between 4 and 11 points? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) The probability the difference is more than 16 points is (Round to four decimal places as needed.)
Government regulations dictate that for any production process involving a certain toxic chemical, the water in the output of the process must not exceed 7920 parts per million (ppm) of the chemical. For a particular process of concern, the water sample was collected by a manufacturer 25 times randomly and the sample average x¯ was 7960 ppm. It is known from historical data that the standard deviation σ is 80 ppm. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) What is the probability that the sample average in this experiment would exceed the government limit if the population mean is equal to the limit? Use the Central Limit Theorem. The probability is (Round to four decimal places as needed.)
The heights of 1000 students are approximately normally distributed with a mean of 172.6 centimeters and a standard deviation of 7.2 centimeters. Suppose 300 random samples of size 25 are drawn from this population and the means recorded to the nearest tenth of a centimeter. Complete parts (a) through (c) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Determine the mean and standard deviation of the sampling distribution of X¯. The mean is μx― = (Type an integer or a decimal. Do not round.) The standard deviation is σX― = . (Type an integer or a decimal. Do not round.) (b) Determine the expected number of sample means that fall between 169.9 and 173.8 centimeters inclusive. sample means (Round to the nearest whole number as needed.) (c) Determine the expected number of sample means falling below 169.5 centimeters. sample means (Round to the nearest whole number as needed.)