BackFor a new advertising campaign, a video game retailer is interested in including information on the average play time of their most popular game. They get 100 random samples of 40 players and obtain their play time to get a sampling distribution. The mean of the sampling distribution is 26.7 hours. In this example, what is the value of ?
Graphical Analysis In Exercises 9 and 10, the graph of a population distribution is shown with its mean and standard deviation. Random samples of size 100 are drawn from the population. Determine which of the figures labeled (a)–(c) would most closely resemble the sampling distribution of sample means. Explain your reasoning.
The waiting time (in seconds) to turn left at an intersection
Under what conditions is the sampling distribution of x̄ normal?
In Exercises 55–60, find the indicated probabilities and interpret the results.
Refer to Exercise 34. A random sample of six days is selected. Find the probability that the mean surface concentration of carbonyl sulfide for the sample is (a) between 5.1 and 15.7 picomoles per liter. Compare your answers with those in Exercise 34.
In Exercises 55–60, find the indicated probabilities and interpret the results.
The mean annual salary for Level 1 actuaries in the United States is about \$72,000. A random sample of 45 Level 1 actuaries is selected. What is the probability that the mean annual salary of the sample is (a) less than \$75,000? Assume sigma = \$11,000.
In Exercises 55–60, find the indicated probabilities and interpret the results.
Refer to Exercise 33. A random sample of 2 years is selected. Find the probability that the mean amount of greenhouse gases for the sample is (a) less than 5500 MMT CO2 eq. Compare your answers with those in Exercise 33.
In Problems 23 through 26, indicate whether a confidence interval for a proportion or mean should be constructed to estimate the value of the variable of interest. Justify your response.
A developmental mathematics instructor wishes to estimate the typical amount of time students dedicate to studying mathematics in a week. She asks a random sample of 50 students enrolled in developmental mathematics at her school to report the amount of time spent studying mathematics in the past week.
In Exercises 55–60, find the indicated probabilities and interpret the results.
The mean annual salary for physical therapists in the United States is about \$87,000. A random sample of 50 physical therapists is selected. What is the probability that the mean annual salary of the sample is (a) less than \$84,000? Assume sigma = \$10,500.
In Exercises 55–60, find the indicated probabilities and interpret the results.
The mean MCAT total score in a recent year is 500.9. A random sample of 32 MCAT total scores is selected. What is the probability that the mean score for the sample is (b) more than 502? Assume sigma=10.6.
Long Life? In a survey of 35 adult Americans, it was found that the mean age (in years) that people would like to live to is 87.9 with a standard deviation of 15.5. An analysis of the raw data indicates the distribution is skewed left.
a. Explain why a large sample size is necessary to construct a confidence interval for the mean age that people would like to live.
"Old Faithful The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between eruptions is approximately normal with standard deviation 21.25 minutes, answer the following questions: Source: www.unmuseum.org
e. On a certain day, suppose there are 22 time intervals for Old Faithful. Treating these 22 eruptions as a random sample, the likelihood the mean length of time between eruptions exceeds _______ minutes is 0.20."
Assume the machine shifts and the distribution of the amount of the compound added now has a mean of 9.96 milligrams and a standard deviation of 0.05 milligram. You select one vial and determine how much of the compound was added.
b. You randomly select 15 vials. What is the probability that you select at least one vial that is within the acceptable range?
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a. Find the t-value such that the area in the right tail is 0.10 with 25 degrees of freedom.
b. Find the t-value such that the area in the right tail is 0.05 with 30 degrees of freedom.
"Answer the following questions for the sampling distribution of the sample mean shown to the right.
c. If the sample size is n = 16, what is the standard deviation of the population from which the sample was drawn?"