Suppose x has a distribution with a mean of 90 and a standard deviation of 27. Random samples of size n36 are drawn. A USE SALT (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has an approximately normalv distribution with mean and standard deviation . (b) Find the z value corresponding to x94.5. (c) Find P(x< 94.5). (Round your answer to four decimal places.) P < 94.5) -
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- Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X>36) Which of the following normal curves corresponds to P(X>36)? A. 36 50 A normal curve has a horizontal axis with two labeled coordinates, 36 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 36 and 50. The area under the curve between the vertical line segments is shaded. B. 36 50 A normal curve has a horizontal axis with two labeled coordinates, 36 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 36 and 50. The area…A survey collected data from a random sample of 121 people living in Jade city. The sample average of the distance people travel to reach their workplaces (Y) is 23.28 km and the standard deviation (sy) is 7.48 km. The standard error of the sample average of the distance people travel to reach their workplaces is 68 km. (Round your answer to two decimal places.) Let μy denote the mean of the distance all the people in Jade city travel to reach their workplaces. The p-value of the test Ho: #y #22 km vs. H₁: Hy #22 km is (Round your answer to two decimal places.)The life of a butterfly is normally distributed with a mean of 50 days. You took a random sample of 25 such butterflies. The mean life for this sample is 47 days a standard deviation of 3 days. At α = 0.05. a. Test to see if the average life of a butterfly is different from 50 days. b. Your friend believes that the life of a butterfly is less than 50 days. Is she correct?
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- Assume that we have estimated the standard deviation of a sample x₁,. ., xn ER using the sample standard deviation s = ô(x₁,x2,...,xn). What does ô(−2x1, −2x2,..., -2xn) equal? A: s B: -4s C: 4s D: -2s E: 2sSuppose 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(Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (1) 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) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ο Hg: μ= 4.64; H1: μ 4.64 Ο Ηρ: μ> 4.64; H1: μ = 4.64 Ho: u = 4.64; H1: u * 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O…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(Assume the random variable X is normally distributed with a mean of 130 and standard deviation of 21.5. State answers to THREE decimals. P (140 < x < 165) = P( x > 105) =Let Xbe normally distributed with mean u=2.5 and standard deviation o = 1.8. [You may find it useful to reference the z table.] a. Find PX> 6.5). (Round your final answer to 4 decimal places.) P(X>6.5) b. Find A5.5 sXs7.5). (Round your final answer to 4 decimal places.) P(5.5 sXs7.5) c. Find x such that PX> x) = 0.0869. (Round your final answer to 3 decimal places.) b. Find P5.5 sXs7.5). (Round your final answer to 4 decimal places.) P(5.5 sXs7.5) c. Find x such that PX> x) = 0.0869. (Round your final answer to 3 decimal places.) d. Find x such that P(xs Xs 2.5) = 0.1255. (Negative value should be indicated by a minus sign. Round your final answer to 3 decimal places.)SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. 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