Regardless of the shape of the population, the sampling distribution of the mean approaches a normal distribution as sample size increases А. True В. False
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- In China, 4-year-olds average 3 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5 hours and the amount of time spent alone is normally distributed. We randomly survey one Chinese 4-year-old living in a rural area. We are interested in the amount of time the child spends alone per day.Give the distribution of X.X ~Steve, the underpaid graduate student, is interested in determining how many final grades in Dr. Boehring’sclass vary. Steve determines that the standard deviation of final grades in Dr. Tahkstumusch’s class is 7. Steve takes a random sample of 50 final grades from Dr. Boehring’s class and computes a standard deviation of 9.Assume that the final grades in Dr. Boehring’s class are normally distributed. At the 5% significance level, do the data provide sufficient evidence to conclude that the standard deviationσof final grades in Dr. Boehring’sclass are greater than 7? Use the rejection region approach for all of the parts below. (a) Define the appropriate hypotheses (b)State and verify that the proper assumptions hold (c)Use the rejection region approach to perform the test (d) Provide support for your decision regarding the null hypothesis (e) Write a summary of your conclusion in the context of the problemThe weight in kilograms of the citizens of Fredonia has a mean of 50 kg and standard deviation of 24 kg (a) Find the mean of the sampling distribution of the sample mean. (b) Find the standard deviation of the sampling distribution of the sample mean.
- Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score greater than 0.96. Sketch the region. Choose the correct graph below. О А. В. D. -0.96 0.96 0.96 0.96 -0.96A company's single-serving cereal boxes advertise 1.63 ounces of cereal. In fact, the amount of cereal X in a randomly selected box can be modeled by a Normal distribution with a mean of 1.70 ounces and a standard deviation of 0.03 ounces. Let Y = the excess amount of cereal beyond what's advertised in a randomly selected box, measured in grams (1 ounce = 28.35 grams). A. Find the mean of Y B. Calculate and interpret the standard deviation of Y C. Find the probability of getting at least 1 gram more cereal than advertisedHeight and weight are two measurements used to track a child's development. An organization measures child development by comparing the weights of children who are the same height and the same gender. In a certain year, weights for all 80 cm girls in the reference population had a mean ? = 11.8 kg and standard deviation ? = 0.6 kg. Weights are normally distributed. X ~ N(11.8, 0.6). Calculate the z-scores that correspond to the following weights and interpret them. (Round your numerical answers to two decimal places.) (a) 12.4 kg z = _______ A child who weighs 12.4 kg is standard deviation(s) [above/below] the mean of 11.8 kg. (b) 10.1 kg z = _______ A child who weighs 10.1 kg is standard deviation(s) [above/below] the mean of 11.8 kg. (c) 13.3 kg z = ________ A child who weighs 13.3 kg is standard deviation(s) [above/below] the mean of 11.8 kg.
- Suppose the masses of a batch of 2000 potatoes have a mean of 60 grams with a standard deviation of 8 grams. Assuming the weights have a normal distribution, predict the number of potatoes that would have masses between 45 and 55 grams. Sketch the distribution curve, shade the required probability, and show horizontal scales the population parameters and the z-scores. Solve the problemA company produces steel rods. The lengths of the steel rods are distributed with a mean of 102.3-cm and a standard deviation of 2-cm. For shipment, 7 steel rods are bundled together. Round all answers to four decimal places if necessary. Note: When writing the distributions, they should be of the form (mean, variance) a. What is the distribution of X? X ~ ( b. What is the distribution of X? X~ N( c. For a single randomly selected steel rod, find the probability that the length is between 102.5-cm and 103.5-cm. d. For a bundled of 7 rods, find the probability that the average length is between 102.5-cm and 103.5- cm. e. For part d), is the assumption of normal necessary? Yes NoThe noon-day temperature (in °C) in Ajax last winter can be represented by the normal distribution X~N( 6, 62). How often was it above - 3°C at noon in Ajax last winter? Make a sketch.
