For items 1-3, please refer to the problem below:The average grade of the students in Statistics is 87 with a standard deviation of 2.15. Assumethat thevariable is normally distributed.1. What is the probability that the grade of a student is greater than 90?2. If a student is selected at random, what is the probability that the grade of the studentwill be below 86?3. If a random sample of 50 students is chosen, what is the probability that the averagegrade is not less than 858

Answered: Image /qna-images/answer/af33a88a-4896-4bf3-bb7a-ee9d5cc6ca4a.jpg

Answered: For items 1-3, please refer to the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that the number of points scored in a game comes from a normal population with an average of 12 points and a standard deviation of 9 points. Estimate the chance that the average points scored in ten randomly selected games will exceed 14.2 points. A. 0.4034 B. 0.0073 C. 0.2198 D. 0.2297
A particular fruit's weights are normally distributed, with a mean of 442 grams and a standard deviation of 35 grams. If you pick 9 fruits at random, then 10% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.
1. The test scores of an Engineering Mechanics class with 800 students are distributed normally with a mean of 75 and a standard deviation of 7. a. What percentage of the class has a test score between 68 and 82? b. Approximately how many students have a test score between 61 and 89? c. What is the probability that a student chosen at a random has a test score between 54 and 75? d. Approximately how many students have a test score greater than or equal 96
Consider the data from the Anthropology 105 class. The mean for women is 64.33 in and the standard deviation is 2.64 in. The average height of men in the US is approximately 5ft 10in. What proportion of women represented here are shorter than the average man?
Assume that in a given year the mean mathematics SAT score was 495, and the standard deviation 111. A sample of 61 score is chosen. ANSWER ALL QUESTIONS PLEASE SHOW WORK A.What is the probability that same mean score is less than 484? B. The probability that the sample mean score is between 460 and 500 is? C. The 10th percentile of the sample mean is D. Would it be unusual if the sample mean were greater than 520? And what is the probability? E. Do you think it would be unusual for an individual to get a score greater than 520? What is the probability
For numbers 31-37, refer to the given problem. The average time it takes for a group of college students to complete a certain examination is 46.2 minutes whereas the standard deviation is 8 minutes. Fifty college students were randomly selected to take the examination. Assume that the variable is normally distributed. What is the probability that the mean. time it takes for the group to complete the test will be less than 43 minutes? 32. Wnar B. 45 33 A. & 34. What is asked in the given problem? A. P(X 43) B. P(43) 35. What formula is to be used in finding the z-score? D. z = 4 Vi A. z = -X B. z = C. z = 36. What is the answer to the question? B. 15.54% A. 0.23% C. 23% D. 34.46%
Please show the steps to solve the problems 28 a, b, and c.
A particular fruit's weights are normally distributed, with a mean of 271 grams and a standard deviation of 28 grams.If you pick 3 fruits at random, then 7% of the time, their mean weight will be greater than how many grams?Give your answer to the nearest gram.
A particular fruit's weights are normally distributed, with a mean of 317 grams and a standard deviation of 29 grams. If you pick 25 fruits at random, then 5% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.
Suppose that the number of Facebook friends users have is normally distributed with a mean of 149 and a standard deviation of about 41. Assume fifteen individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. a. What is the distribution of x̄? x̄ - N -----------, ---------- b. For the group of 15, find the probability that the average number of friends is less than 156. ------------- c. Find the first quartile for the average number of Facebook friends. Round to 2 decimals places. --------------- d. For part b), is the assumption that the distribution is normal necessary? ------------No, --------- yes
For numbers 31-37, refer to the given problem. The average time it takes for a group of college students to complete a certain examination is 46.2 minutes whereas the standard deviation is 8 minutes. Fifty college students were randomly selected to take the examination. Assume that the variable is normally distributed. What is the probability that the mean time it takes for the group to complete the test will be less than 43 minutes? 31. What is the population mean u? B. 43 A. 8 C. 46.2 D. 50 32. What is the population standard deviation a? А. 8 В. 43 C. 46.2 D. 50 33. What is the sample size n? А. 8 B. 43 C. 46.2 D. 50 34. What is asked in the given problem? A. P(X 43) D. P(>43) 35. What formula is to be used in finding the z-score? D. z = X-4 VIL H-X B. Z = X- C. z = -8 A. z = of 36. What is the answer to the question? В. 15.54% A. 0.23% С. 23% D. 34.46%
answer A, C, and D

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