Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 6,000 pounds and the standard deviation is 150 pounds. Assume that the population follows the normal distribution. Forty trucks are randomly selected and weighed. Within what limits will 95 percent of the sample means occur?

The mean amount purchased by a typical customer at Churchill’s Grocery Store is $23.50, with a standard deviation of$5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions. a. What is the likelihood the sample mean is at least $25.00? b. What is the likelihood the sample mean is greater than$22.50 but less than $25.00? c. Within what limits will 90 percent of the sample means occur?

The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.8 years. The standard deviation of the distribution is 2.5 years. For a random sample of 60 men, what is the likelihood that the age at which they were married for the first time is less than 25.1 years?

In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.5 hours per week playing organized sports. The population’s standard deviation is 2.2 hours per week. Based on a sample of 121 students, Healthy Lifestyles Incorporated would like to apply the central limit theorem to make various estimates. a. Compute the standard error of the sample mean. b. What is the chance HLI will find a sample mean between 5 and 6 hours? c. Calculate the probability that the sample mean will be between 5.3 and 5.7 hours. d. How strange would it be to obtain a sample mean greater than 6.5 hours?

Nike’s annual report says that the average American buys 6.5 pairs of sports shoes per year. Suppose the population standard deviation is 2.1 and that a sample of 81 customers will be examined next year. a. What is the standard error of the mean in this experiment? b. What is the probability that the sample mean is between 6 and 7 pairs of sports shoes? c. What is the probability that the difference between the sample mean and the population mean is less than 0.25 pairs? d. What is the likelihood the sample mean is greater than 7 pairs?

A variable of a population has a normal distribution. Suppose that you want to find a confidence interval for the population mean. a. If you know the population standard deviation, which procedure would you use? b. If you do not know the population standard deviation, which procedure would you use?

Mattel Corporation produces a remote-controlled car that requires three AA batteries. The mean life of these batteries in this product is 35.0 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.5 hours. As a part of its testing program, Sony tests samples of 25 batteries. a. What can you say about the shape of the distribution of the sample mean? b. What is the standard error of the distribution of the sample mean? c. What proportion of the samples will have a mean useful life of more than 36 hours? d. What proportion of the sample will have a mean useful life greater than 34.5 hours? e. What proportion of the sample will have a mean useful life between 34.5 and 36.0 hours?

Suppose your statistics instructor gave six examinations during the semester. You received the following grades: 79, 64, 84, 82, 92, and 77. Instead of averaging the six scores, the instructor indicated he would randomly select two grades and compute the final percent correct based on the two percents. a. How many different samples of two test grades are possible? b. List all possible samples of size two and compute the mean of each. c. Compute the mean of the sample means and compare it to the population mean. d. If you were a student, would you like this arrangement? Would the result be different from dropping the lowest score? Write a brief report.

AA batteries are made by Power + Inc. and are used in remote-control toy cars. The average life of these batteries is 35.0 hours, with a standard deviation of 5.5 hours, and it follows the normal probability distribution. 25 battery samples are tested as part of Power + Inc.'s quality assurance methodology. What proportion of the samples will have a mean useful life greater than 34.5 hours?

For Division I student-athletes, the mean performance score on a physical fitness test was 947, with a standard deviation of 205. How likely is it that a random sample of 60 of these students will have a mean below 900?

Bob Nale is the owner of Nale’s Quick Fill. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a population standard deviation of 2.30 gallons. From his records, he selects a random sample of 60 sales and finds the mean number of gallons sold is 8.60. a. What is the point estimate of the population mean? b. Develop a 99 percent confidence interval for the population mean. c. Interpret the meaning of part (b).

The number of pizzas delivered to university students each month is a random variable with the following probability distribution.

Find the probability that a student has received delivery of two or more pizzas this month.

A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as

$$\begin{aligned} &H_{1}: \mu=3000 \text { grams }\\ &H_{a}: \mu \leq 2999 \text { grams } \end{aligned}$$

Identify the following expenditures as capital expenditures or revenue expenditures:
f. Original life of the delivery truck had been estimated at four years, and straight-line depreciation of 25 percent yearly had been recognized. After three years' use, however, it was decided to recondition the truck thoroughly, including adding a new engine.