BackIn 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.
A certain stock's daily percent return on Fridays has a mean of 3.12% and a standard deviation of 41.25%. If random samples of 40 days are selected and the mean return for each sample is calculated, what is the probability that a sample mean is greater than 17%?
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
Finding Probabilities for Sampling Distributions In Exercises 29–32, find the indicated probability and interpret the results.
Dow Jones Industrial Average From 1975 through 2020, the mean annual gain of the Dow Jones Industrial Average was 652. A random sample of 32 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 700? Assume sigma=1540
Finding Probabilities for Sampling Distributions In Exercises 29–32, find the indicated probability and interpret the results.
Asthma Prevalence by State The mean percent of asthma prevalence of the 50 U.S. states is 9.51%. A random sample of 30 states is selected. What is the probability that the mean percent of asthma prevalence for the sample is greater than 10%? Assume sigma=1.17%
Which Is More Likely? Assume that the fertility rates in Exercise 32 are normally distributed. Are you more likely to randomly select a state with a fertility rate of less than 65 or to randomly select a sample of 15 states in which the mean of the state fertility rates is less than 65? Explain.
"[NW] Oil Change The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is skewed right. However, records indicate that the mean time for an oil change is 11.4 minutes, and the standard deviation for oil-change time is 3.2 minutes.
a. To compute probabilities regarding the sample mean using the normal model, what size sample would be required?"
"Reading Rates The reading speed of second-grade students is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm.
d. What effect does increasing the sample size have on the probability? Provide an explanation for this result."
"Upper Leg Length The upper leg length of 20- to 29-year-old males is approximately normal with a mean length of 43.7 cm and a standard deviation of 4.2 cm.
Source: “Anthropometric Reference Data for Children and Adults: U.S. Population, 1999–2002”; Volume 361, July 7, 2005.
e. A random sample of 15 males who are 20–29 years old results in a mean upper leg length of 46 cm. Do you find this result unusual? Why?"
"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?"
"Answer the following questions for the sampling distribution of the sample mean shown to the right.
b. What is the value of σx̄?"
"Answer the following questions for the sampling distribution of the sample mean shown to the right.
a. What is the value of μx̄?"
True or False: To cut the standard error of the mean in half, the sample size must be doubled.
The __________ of the sample mean, x̄, is the probability distribution of all possible values of the random variable x̄ computed from a sample of size n from a population with mean μ and standard deviation σ.
Suppose a simple random sample of size n is drawn from a large population with mean μ and standard deviation σ. The sampling distribution of x̄ has mean μx̄ = _________ and standard deviation σx̄ = ________.