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o A robot executes a "random walk" in the following way: Each minute it takes a step north or south, with probability - each, and its successive step directions are independent. The length of each step is 50 cm. Use the central limit theorem to approximate the probability distribution of its location after 1 hour. Where is the robot most likely to be?

o A robot executes a "random walk" in the following way: Each minute it takes a step north or south, with probability - each, and its successive step directions are independent. The length of each step is 50 cm. Use the central limit theorem to approximate the probability distribution of its location after 1 hour. Where is the robot most likely to be?

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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o A robot executes a "random walk" in the following way: Each minute it takes a step north or south, with probability - each, and its successive step directions are independent. The length of each step is 50 cm. Use the central limit theorem to approximate the probability distribution of its location after 1 hour. Where is the robot most likely to be? 2. A maker of a certain brand of low-fat cereal bars claims that the average saturated fat content is 0.4 gram. In a random sample of 8 cereal bars of this brand, the saturated fat content was as shown below. 0.7 0.3 0.6 0.5 0.4 0.7 0.3 0.3 Would you agree with the claim? Assume a normal distribution. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. The computed t-value is t=, so P(T>t) is This V evidence to disagree with the claim. (Round to two decimal places as needed.) 3 Given a random sample of size 23 from a normal distribution, find k such that (a) P(- 2.508 < T<k) = 0.94. (b) Find P(k<T<3.119) = 0.0225. (c) Find P(-k<T<k)= 0.80. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. (a) k = 1.717 (Round to three decimal places as needed.) (b) k= 2.074 (Round to three decimal places as needed.) (c) k = (Round to three decimal places as needed.)
Transcribed Image Text:o A robot executes a "random walk" in the following way: Each minute it takes a step north or south, with probability - each, and its successive step directions are independent. The length of each step is 50 cm. Use the central limit theorem to approximate the probability distribution of its location after 1 hour. Where is the robot most likely to be? 2. A maker of a certain brand of low-fat cereal bars claims that the average saturated fat content is 0.4 gram. In a random sample of 8 cereal bars of this brand, the saturated fat content was as shown below. 0.7 0.3 0.6 0.5 0.4 0.7 0.3 0.3 Would you agree with the claim? Assume a normal distribution. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. The computed t-value is t=, so P(T>t) is This V evidence to disagree with the claim. (Round to two decimal places as needed.) 3 Given a random sample of size 23 from a normal distribution, find k such that (a) P(- 2.508 < T<k) = 0.94. (b) Find P(k<T<3.119) = 0.0225. (c) Find P(-k<T<k)= 0.80. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. (a) k = 1.717 (Round to three decimal places as needed.) (b) k= 2.074 (Round to three decimal places as needed.) (c) k = (Round to three decimal places as needed.)
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