Find E[X], and Var[X], when "X" is a normal random variable with pa- rameter µ and o? respectively.
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- Assume that we have two normal distributions both with means 0 and standard deviations σ1 and σ2. If σ1 ≥ σ2, then which of P (0 ≤ x ≤ σ1) and P (0 ≤ x ≤ σ2) is bigger? Explain your answer.Recall that Benford's Law clalms that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a v leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millons of numbers in a large computer data bank. You draw a random sample of n = 229 numbers from this file and r 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. large data file, the probability of getting a number with "1" as the () Test the dalm that p is more than 0.301. Use a 0.10. (a) what is the level of signifcance? State the null and alternate hypotheses. O Hg: p = 0.301; H p> 0.301 O Hgi P = 0.301; Hip 0.301; Hp- 0.301 O Ho: P= 0.301; H: p- 0.301 (b) what sampling distribution will you use? O The Student's t, since np > 5 and ng > 5. O The…A person's level of blood glucose and diabetes are closely related. Let x be a random variablemeasured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a12-hour fast, the random variable x will have a distribution that is approximately normal withmean μ = 84 and standard deviation of σ = 26 What is the probability that, for an adult after a12-hour fast, x is less than 81? Group of answer choices 0.546 0.454 0.023 0.273 0.227
- Let m denote margin of error, n sample size and σ standard deviation. m= zα/2(σn) Solve the above equation for n.Assume the random variable X is normally distributed with a mean of μ=50μ=50and a standard deviation of σ=7.σ=7.Compute and find the probability P(X>35).You obtain a t comp of .975 in a two sample independent t test with alpha at .05. Is it significant?
- Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(Tyson Corp. stock has returns of 3%, 18%, -24%, and 28% for the past four years. Based on this information, what is the 99% probability range for any one given year? Select one: Oa 24.5 to 34.3% O b.-61.7 to 74.2% OC.-8.4 to 11.7% Od.-16.4 to 28.9% e. 39.0 to 51.5%A random sample of size n = 28 is obtained from a normally distributed population with a population mean of u = 350 and a variance of o =145. a. What is the probability that xr < 345? b. What is the probability that the sample variance is less than 140? c. What is the probability that the sample variance is greater than 175?Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(A random sample of size 36 from a population with known variance, o = 9, yields a sample mean of x = 17. Find ß, for testing the hypothesis H,: u = 15 versus H1 : =16. Assume a 0.05. %3D %3DLet x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave the following information. Σχ - 64.2; Σ ? = 528.24; Ey = 90.4; Ey² = 1063.88; Exy = 741.77 6.2 8.6 7.0 7.5 8.3 6.9 10.0 9.7 y 9.7 10.3 10.9 11.5 14.2 7.0 14.6 12.2 Find the equation of the least-squares line. (Round your answers to three decimal places.) Find the sample correlation coefficient r and the sample coefficient of determination r. (Round your answers to three decimal places.) r = 2 = If x = 7.0, use the least-squares line to predict y. (Round your answer to two decimal places.) y = Find an 80% confidence interval for your prediction. (Round your answers to two decimal places.) lower limit mg/10 ml upper limit mg/10 ml Use level of significance 1% and test the claim that the…SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON