2. A statistics professor has office hours from 9:00 AM to 10:00 AM each day. The number of students waiting to see the professor is a random variable X with the distribution show below: x P (X = x) 0 0.05 1 0.10 2 0.40 3 0.25 4 0.15 5 0.05

Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is given in Table P(x) 3 0.05 4 0.40 5 0.30 6 0.15 7 0.10 Table a. In words, define the random variable X. b. What does it mean that the values zero, one, and two are not included for x in the PDF?

Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 17 16 18 15 12 14 17 17 11 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = s = (ii) Does this information indicate that the population average HC for this patient is higher than 14? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. a: μ = 14; H1: μ < 14 b: μ = 14; H1: μ ≠ 14 c: μ > 14; H1: μ = 14 d: μ < 14; H1: μ = 14 e: μ = 14; H1: μ > 14 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume…

A company produces 10,000 plastic papers per day. This company supplies papers to a shops which sells them in packs of 10 cups per pack. If less than two of a randomly selected pack (of 10 cups) from the order are defective, the shop accepts the whole order. The proportion of defective papers produced by the manufacturing company is 10%. Let ? be the random variable representing the number of defective cups in a pack. i. Identify the type of distribution being described in this question and write down the value/s of its parameter/s. ii. What is the probability that the order will be accepted?

Give the percent of scores between the mean and the z-value of normally distributed random variable. a 1) 1.25

Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.336 0.296 0.340 0.248 0.367 0.269 y 3.2 7.5 4.0 8.6 3.1 11.1 (b) Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.) t   critical t ±   (d) Find the predicted percentage of strikeouts for a player with an x = 0.288 batting average. (Use 2 decimal places.) %(e) Find a 95% confidence interval for y when x = 0.288. (Use 2 decimal places.) lower limit  % upper limit  % (f) Use a 10% level of significance to test the claim that β ≠ 0. (Use 2 decimal places.) t   critical t ±   (g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit   upper limit   please show steps and work

1. Identify if the following scenarios describe a discrete or continuous random variable. Explain your choice. (a) X = The number of persons in an emergency room 181screte (b) W = The weights of delivery trucks at a supermarket. Lconinaas (c) H= The areas of houses being built in a new subdivision. 2. Faith is a 95% free throw shooter. At practice, each player shoots 20 free throws. L X the number of free throws Faith makes out of 20 shots. (a) Explain why X is a binomial random variable. (b) Calculate the mean of X. (c) Calculate the standard deviation of X. (d) Use the binomial probability formula to find P(X = 19). Interpret this value in context. (e) Her coach says that he will let the team out of practice early if Faith makes 18 or me free throws. What is the probability that practice ends early? Show your work. 2017 BFW Publishers Starnes/Tabor Statistics and Probability with Applications 3/e

High school students in Michigan sometimes get "snow days" in the winter when the roads are so bad that school is canceled for the day. Define the random variableX = the number of snow days at a certain high school in Michigan for a randomly selected school year. Suppose the table below gives the probability distribution of X. 1. Value x, 1. 3 4 5 6 7 8 9 10 Probability p, ? 0.19 0.14 0.10 0.07 0.05 0.04 0.04 0.02 0.01 0.01 (a) Write the event “the school year has O snow days" in terms of X. Then find its probability. (b) At this high school, if more than 5 snow days are used over the course of the year, students are required to make up the time at the end of the school year. What's the probability that a randomly selected school year will require make-up days?

When conducting research on allergic reactions to a new drug, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who develop an allergic reaction. x P(x) 0 0.665 1 0.278 2 0.052 3 0.004 4 0.001 5 0.000 a. Find its mean and standard deviation. (Round to one decimal place as needed) b. What is the probability of at least 3 males developing an allergic reaction? (Round to three decimal places as needed)

Consider the population described by the probability distribution shown below. The random variable is observed twice with independent observations. Sample Probability 0.16 0.12 0.04 0.08 0.12 0.09 0.03 0.06 p(x) 0,0 0,2 0,4 0,6 2,0 2,2 2,4 2,6 Full data set 0.4 0.3 4 4,0 4,2 4,4 4,6 Probability 0.04 0.03 0.01 0.02 0.08 0.06 0.02 0.04 0.1 Sample 6,0 6,2 6,4 6,6 0.2 a. Complete the sampling distribution table. Type the x values in ascending order. 1 2 6. Probability 0.16 0.22 0.13 (Type exact answers in simplified form.)