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- c) Answer both of the following: i) Consider a random variable X which is normally distributed with mean zero and unit variance. Using the proper statistical table, find the number z such that P(z < X < 2.64) = 0.4760. Give your answer rounded to 2 decimal places. follows at distribution with (2n + 1) degrees of freedom, i.e. Y ~ t2n+1- ii) A random variable Make use of the appropriate statistical table to get the value of n knowing that P(Y 2 3.1824) = 0.025.A consumer group plans a comparative study of the mean life of four different brands of batteries. Ten batteries of each brand will be randomly selected and the time until the energy level falls below a pre-specified level is measured. a) Which of the following is the appropriate alternative hypothesis for the null hypothesis: H0: μa = μb = μc = μd? (In this problem, μa = mean time of Brand A, μb = mean time of Brand B, etc.) Ha: none of the means are equal Ha: μa ≠ μb ≠ μc ≠ μd Ha: μa ≠ μb, μa ≠ μc, μa ≠ μd, μb ≠ μc, μb ≠ μd, μc ≠ μd Ha: at least one of the means is different b)In order to analyze the data with ANOVA, we need to satisfy the condition of randomization. How do we know that this condition has been met? -One SRS of batteries is selected from a collection of batteries of all brands. -The batteries are randomly allocated to the four brands. -Separate random samples of batteries are selected from each brand.Scores of the first test in Econ 261 follow a normal distribution with mean 70 and standard deviation 5. Compute the following probabilities. P(X2 60) is: O.0228 .9772 O.9862 O:1325
- Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean u = 260 days and standard deviation o = 22 days. Complete parts (a) through (f) below. O B. If 100 pregnant individuals were selected independently from this population, we would expect 37 pregnancies to last less than 253 days. O C. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 253 days. (b) Suppose a random sample of 21 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of x is normal with H; = 260 and o: = 4.8008. (Round to four decimal places as needed.) (c) What is the probability that a random sample of 21 pregnancies has a mean gestation period of 253 days or less? The probability that the mean of a random sample of 21 pregnancies is less than 253 days is approximately 0.0724. (Round to four decimal places as needed.)…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(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(10. An atom of Uranium-238 is unstable and will eventually decay (i.e., emit a particle and turn into a different element). Given an atom of Uranium-238, the time elapsed until it decays, in years, is modeled as an Exponential random variable with parameter 1 = 0.000000000155. How many years must pass for there to be a 50% chance that the Uranium atom decays?Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0μ=74.0 beats per minute and a standard deviation of sigma equals 12.5σ=12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 7777 beats per minute.a) b) c)Recommended 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