In 1905, R. Pearl published the article "Biometrical Studies on Man. I. Variation and Correlation in Brain Weight" (Biometrika, Vol. 4, pp. 13-104). According to the study, brain weights of Swedish men are normally distributed with mean 1.40 kg and standard deviation 0.11 kg. Apply the empirical rule to fill in the blanks.

a. Approximately 68 % of Swedish men have brain weights between and

b. Approximately 95 % of Swedish men have brain weights between __ and

c. Approximately 99.7 % of Swedish men have brain weights between and

d. Draw graphs to portray your results.

Do the following parts: (i) consider the given matrix as the coefficient matrix A of the system $\mathbf{x}^{\prime}=\mathbf{A} \mathbf{x}$ and use Theorem to determine the classification of the origin; (ii) use one of the computer programs to draw the vector field for each system $\mathbf{x}^{\prime}=\mathbf{A} \mathbf{x}$ and some trajectories for various initial conditions.

$$\left[\begin{array}{ll} 1 & 0 \\ 4 & 3 \end{array}\right]$$

Suppose the exchange rate between the U.S. dollar and the Swedish krona was 8 52 krona=$1, and the exchange rate between the dollar and the British pound was$£ 1=$1.53$. What would be the exchange rate between Swedish kronas and pounds?

In Children’s Hospital in Seattle, there are, on average, 60 births per week. Mothers and babies stay, on average, two days before they leave the hospital. In Swedish Hospital (also in Seattle), the average number of births per week is 210. Mothers and children stay in the hospital two days, on average. How many new mothers are staying in Swedish Hospital?

Determine whether the following statement is true: When random samples of 50 men and 50 women are obtained and we want to test the claim that men and women have different mean annual incomes, there is no need to confirm that the samples are from populations with normal distributions.

An oil company that has two refineries needs at least 8000, 14,000, and 5000 barrels of low-, medium-, and high-grade oil, respectively. Each day, Refinery I produces 2000 barrels of low-, 3000 barrels of medium-, and 1000 barrels of high-grade oil, whereas Refinery II produces 1000 barrels each of low- and high- and 2000 barrels of medium-grade oil. If it costs $25,000 per day to operate Refinery I and$20,000 per day to operate Refinery II, how many days should each refinery be operated to satisfy the production requirements at minimum cost? What is the minimum cost? (Assume that a minimum cost exists.)

In 1905, R. Pearl published the article "Biometrical Studies on Man. I. Variation and Correlation in Brain Weight" (Biometrika, Vol. 4, pp. 13-104). According to the study, brain weights of Swedish men are normally distributed with a mean of 1.40 kg and a standard deviation of 0.11 kg.

a. Determine the sampling distribution of the sample mean for samples of size 3. Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of three Swedish men.

b. Repeat part (a) for samples of size 12 .

c. Construct graphs.

d. Determine the percentage of all samples of three Swedish men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.40 kg. Interpret your answer in terms of sampling error.

e. Repeat part (d) for samples of size 12.

Which subfield of psychology provides psychology’s contribution to behavioral medicine? a. Cognitive. b. Health. c. Clinical. d. Educational. e. Community.

Suppose an individual is randomly selected from the population of all adult males living in the United States. Let A be the event that the selected individual is over 6 ft in height, and let B be the event that the selected individual is a professional basketball player. Which do you think is larger, $P(A | B)$ or $P(B | A)$? Why?

The heights (in inches) of men have a distribution that is approximately normal, so it appears that those heights are from a normally di tributed population. Are the logarithms of normally distributed heights also normally distributed?

We have provided a scenario for a hypothesis test for a population mean. Decide whether the z-test is an appropriate method for conducting the hypothesis test. Assume that the population standard deviation is known in each case. Preliminary data analyses reveal that the sample data contain no outliers but that the distribution of the variable under consideration is probably highly skewed. The sample size is 24.

AS reported in Rmmer's World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 61 minutes and standard deviation 9 minutes. Let x denote finishing time for finishers in this race. a. Sketch the distribution of the'variable x. b. Obtain the standardized version, z, of x. c. Identify and sketch the distribution of z. d. The percentage of finishers with times between 50 and 70 minutes is equal to the area under the standard normal curve between ____ and ____. e. The percentage of finishers with times less than 75 minutes is equal to the area under the standard normal curve that lies to the ____ of ____.

One of the larger species of tarantulas is the Grammostola mollicoma, whose common name is the Brazilian giant tawny red. A tarantula has two body parts. The anterior part of the body is covered above by a shell, or carapace. From a recent article by F. Costa and F. Perez-Miles titled “Reproductive Biology of Uruguayan Theraphosids” (The Journal of Arachnology, Vol. 30, No. 3, pp. 571-587), we find that the carapace length of the adult male G. mollicoma is normally distributed with a mean of 18.14 mm and a standard deviation of 1.76 mm. Let x denote carapace length for the adult male G. mollicoma. a. Sketch the distribution of the variable x. b. Obtain the standardized version, z, of x. c. Identify and sketch the distribution of z. d. The percentage of adult male G. mollicoma that have carapace length between 16 mm and 17 mm is equal to the area under the standard normal curve between _____ and _____. e. The percentage of adult male G. mollicoma that have carapace length exceeding 19 mm is equal to the area under the standard normal curve that lies to the _____ of _____.

The paper “Are Babies Normal?” by T. Clemons and M. Pagano (The American Statistician, Vol. 53, No. 4, pp. 298-302) focused on birth weights of babies. According to the article, the mean birth weight is 3369 grams (7 pounds, 6.5 ounces) with a standard deviation of 581 grams. a. Identify the population and variable. b. For samples of size 200, find the mean and standard deviation of all possible sample mean weights. c. Repeat part (b) for samples of size 400.