Recent questions in Normal distributions
Normal distributions

A flowerpot accidentally falls off the window of a condominium unit. Your unit is located below where the flowerpot had fallen. Your window measures to be 1.60 m tall, and the time it takes the flowerpot to move past your window is 0.150 s (from the top part to the bottom part of the window). How high from the top of your window did the flowerpot fell off?

Normal distributions

Suppose the ages of students in Statistics 101 follow a normal distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect. A) The expected value of the sample mean is equal to the population’s mean. B) The standard deviation of the sampling distribution is equal to 3 years. C) The shape of the sampling distribution is approximately normal. D) The standard error of the sampling distribution is equal to 0.3 years.

Normal distributions

One bushel of apples from a dwarf apple tree is equal to 42 pounds. Write an expression to find the number of pounds of apples in any number of bushels. If one tree can produce 6 bushels, how many pounds of apples will an orchard of 100 trees produce?

Normal distributions

The college physical education department offered an advanced first aid course last semester. The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below: Robert, 1.10 Juan, 1.70 Susan, -2.00 Joel, 0.00 Jan, -0.80 Linda, 1.60 If the mean score was μ=150μ=150 with standard deviation σ=20,σ=20, what was the final exam score for each student?

Normal distributions

Do men and women differ in their attitudes toward public corruption and tax evasion? This was the question of interest in a study published in Contemporary Economic Policy (Oct. 2010). The data for the analysis were obtained from a representative sample of over 30,000 Europeans. Each person was asked how justifiable it is for someone to (1) accept a bribe in the course of their duties and (2) cheat on their taxes. Responses were measured as 0, 1, 2, or 3, where O = "always justified" and 3 = "never justified." The large-sample Wilcoxon rank sum test was applied in order to compare the response distributions of men and women. a. Give the null hypothesis for the test in the words of the problem. b. An analysis of the "justifiability of corruption" responses yielded a large-sample test statistic of $$z = -14.10$$ with a corresponding p-value of approximately 0. Interpret this result. c. Refer to part b. Women had a larger rank sum statistic than men. What does this imply about gender attitudes. toward corruption? d. An analysis of the "justifiability of tax evasion" responses yielded a large-sample test statistic of $$z = -18.12$$ with a corresponding p-value of approximately 0. Interpret this result. e. Refer to part d. Again, women had a larger rank sum statistic than men. What does this imply about gender attitudes toward tax evasion?

Normal distributions

The following definition is discussed in advanced mathematics courses. $$f(x)=\begin{cases}\ 0 & \text{if} \times \text{is a rational number}\\ 1 & \text{if} \times\text{ is an irrational number}\\ \end{cases}$$ Evaluate $$f(−34), f(−2–\sqrt )$$, and $$\displaystyle{f{{\left(\pi\right)}}}$$.

Normal distributions

Refer to the Journal of Applied Psychology (Jan. 2011) study of the determinants of task performance. In addition to $$x_{1} =$$ conscientiousness score and $$x_{2} = \{1 \text{if highly complex job, 0 if not}\}$$, the researchers also used $$x_{3} =$$ emotional stability score, $$x_{4} =$$ organizational citizenship behavior score, and $$x_{5} =$$ counterproductive work behavior score to model y = task performance score. One of their concerns is the level of multicollinearity in the data. A matrix of correlations for all possible pairs of independent variables follows. Based on this information, do you detect a moderate or high level of multicollinearity? If so, what are your recommendations? $$x_{1}\ x_{2}\ x_{3}\ x_{4}$$ Conscientiousness $$(x_{1})$$ Job Complexity $$(x_{2}).\ 13$$ Emotional Stability $$(x_{3}).\ 62.\ 14$$ Organizational Citizenship $$(x_{4}).\ 24.\ 03.\ 24$$ Counterproductive Work $$(x_{5})-\ .23-\ .23-\ .02-\ .62$$

Normal distributions

Maurice and Lester are twins who have just graduated from college. They have both been offered jobs where their take-home pay would be $2500 per month. Their parents have given Maurice and Lester two options for a graduation gift. Option 1: If they choose to pursue a graduate degree, their parents will give each of them a gift of$35,000. However, they must pay for their tuition and living expenses out of the gift. Option 2: If they choose to go directly into the workforce, their parents will give each of them a gift of $5000. Maurice decides to go to graduate school for 2 years. He locks in a tuition rate by paying$11,500 for the 2 years in advance, and he figures that his monthly expenses will be $1000. Lester decides to go straight into the workforce. Lester finds that after paying his rent, utilities, and other living expenses, he will be able to save$200 per month. Their parents deposit the appropriate amount of money in a money market account for each twin. The money market accounts are currently paying a nominal interest rate of 3 percent, compounded monthly. Lester works during the time that Maurice attends graduate school. Each month, Lester saves $200 and deposits this amount into the$5000 money market account that his parents set up for him when he graduated. If Lester's initial balance is $$u_{0}=5000,u_n$$ is the current month's balance, and $$u_{n−1}$$ is last month's balance, write an expression for un in terms of $$u_{n−1}$$.

Normal distributions

Maurice and Lester are twins who have just graduated from college. They have both been offered jobs where their take-home pay would be $2500 per month. Their parents have given Maurice and Lester two options for a graduation gift. Option 1: If they choose to pursue a graduate degree, their parents will give each of them a gift of$35,000. However, they must pay for their tuition and living expenses out of the gift. Option 2: If they choose to go directly into the workforce, their parents will give each of them a gift of $5000. Maurice decides to go to graduate school for 2 years. He locks in a tuition rate by paying$11,500 for the 2 years in advance, and he figures that his monthly expenses will be $1000. Lester decides to go straight into the workforce. Lester finds that after paying his rent, utilities, and other living expenses, he will be able to save$200 per month. Their parents deposit the appropriate amount of money in a money market account for each twin. The money market accounts are currently paying a nominal interest rate of 3 percent, compounded monthly. At the end of 2 years, Lester receives a raise and decides to save $250 each month. Maurice receives a$5000 graduation gift from his parents and deposits this amount into his money market account. Maurice goes to work and saves $500 each month. Complete the equations below for the money market account balance for each twin. Let the initial balance u0 be the account balance at the end of 2 years. Write an expression for this month's account balance un in terms of un−1. Recall that the interest rate for the account is 3 percent, compounded monthly. Maurice: $$u_{0}= 5248.47, u_{n}=?\ Lester: u_{0}=?, u_{n}=?$$. Normal distributions ANSWERED asked 2021-06-19 Create and conduct a survey in your class. Organize the results in a two-way table. Then create a two-way table that shows the joint and marginal frequencies. Normal distributions ANSWERED asked 2021-06-15 The missing number in the series 1, 4, 27,____, 3125 is: 81 35 729 256 115 Normal distributions ANSWERED asked 2021-06-12 Advances in medical science and healthier lifestyles have resulted in longer life expectancies. The life expectancy of a male whose current age is x years old is $$f(x)=0.0069502\ x^2−1.6357x+93.76 (60\leq x\leq75)$$ years. What is the life expectancy of a male whose current age is 65? A male whose current age is 75? Normal distributions ANSWERED asked 2021-06-10 A city recreation department offers Saturday gymnastics classes for beginning and advanced students. Each beginner class enrolls 15 students, and each advanced class enrolls 10 students. Available teachers, space, and time lead to the following constraints. ∙∙ There can be at most 9 beginner classes and at most 6 advanced classes. ∙∙ The total number of classes can be at most 7. ∙∙ The number of beginner classes should be at most twice the number of advanced classes. a. What are the variables in this situation? b. Write algebraic inequalities giving the constraints on the variables. c. The director wants as many children as possible to participate. Write the objective function for this situation. d. Graph the constraints and outline the feasible region for the situation. e. Find the combination of beginner and advanced classes that will give the most children a chance to participate. f. Suppose the recreation department director sets new constraints for the schedule of gymnastics classes. ∙∙ The same limits exist for teachers, so there can be at most 9 beginner and 6 advanced classes. ∙∙ The program should serve at least 150 students with 15 in each beginner class and 10 in each advanced class. The new goal is to minimize the cost of the program. Each beginner class costs$500 to operate, and each advanced class costs \$300. What combination of beginner and advanced classes should be offered to achieve the objective? .

Normal distributions

For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic. $$\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline f(x) & 2 & 4.079 & 5.296 & 6.159 & 6.828 & 7.375 & 7.838 & 8.238 & 8.592 & 8.908 \\ \hline \end{array}$$

Normal distributions

1) If A and B are mutually exclusive events with $$P(A) = 0.3$$ and $$P(B) = 0.5$$, then $$P(A\cap B)=?$$ 2) An experiment consists of four outcomes with $$P(E_1)=0.2,P(E_2)=0.3,$$ and $$P(E_3)=0.4$$. The probability of outcome $$E_4$$ is ? 3) If A and B are mutually exclusive events with $$P(A) = 0.3$$ and $$P(B) = 0.5$$, then $$P(A\cap B) =?$$ 4) The empirical rule states that, for data having a bell-shaped distribution, the percentage of data values being within one standard deviation of the mean is approximately 5) If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is ?

Normal distributions

Is it true that girls perform better than boys in the study of languages and so-called soft sciences? Here are several Advanced Placement subjects and the percent of examinations taken by female candidates in 2007: English Language/Composition, 63%; French Language, 70%; Spanish Language, 64%; and Psychology, 65%. (a) Explain clearly why we cannot use a pie chart to display these data, even if we know the percent of exams taken by girls for every subject. (b) Make a bar graph of the data. Order the bars from tallest to shortest; this will make comparisons easier. (c) Do these data answer the question about whether girls perform better in these subject areas? Why or why not?

Normal distributions

Use the following Normal Distribution table to calculate the area under the Normal Curve (Shaded area in the Figure) when $$Z=1.3$$ and $$H=0.05$$; Assume that you do not have vales of the area beyond $$z=1.2$$ in the table; i.e. you may need to use the extrapolation. Check your calculated value and compare with the values in the table $$[for\ z=1.3\ and\ H=0.05]$$. Calculate your percentage of error in the estimation. How do I solve this problem using extrapolation? $$\begin{array}{|c|c|}\hline Z+H & Prob. & Extrapolation \\ \hline 1.20000 & 0.38490 & Differences \\ \hline 1.21000 & 0.38690 & 0.00200 \\ \hline 1.22000 & 0.38880 & 0.00190 \\ \hline 1.23000 & 0.39070 & 0.00190 \\ \hline 1.24000 & 0.39250 & 0.00180 \\ \hline 1.25000 & 0.39440 & 0.00190 \\ \hline 1.26000 & 0.39620 & 0.00180 \\ \hline 1.27000 & 0.39800 & 0.00180 \\ \hline 1.28000 & 0.39970 & 0.00170 \\ \hline 1.29000 & 0.40150 & 0.00180 \\ \hline 1.30000 & 0.40320 & 0.00170 \\ \hline 1.31000 & 0.40490 & 0.00170 \\ \hline 1.32000 & 0.40660 & 0.00170 \\ \hline 1.33000 & 0.40830 & 0.00170 \\ \hline 1.34000 & 0.41010 & 0.00180 \\ \hline 1.35000 & 0.41190 & 0.00180 \\ \hline \end{array}$$

Normal distributions

Suppose that you want to perform a hypothesis test to compare several population means, using independent samples. In each case, decide whether you would use the one-way ANOVA test, the Kruskal-Wallis test, or neither of these tests. Preliminary data analyses of the samples suggest that the distributions of the variable are not normal and have quite different shapes.

Normal distributions