The average amount of money spent for lunch per person in the college cafeteria is $7.39 and the standard deviation is$2.94. Suppose that 41 randomly selected lunch patrons are observed. Assume the distribution of money spent isnormal, and round all answers to 4 decimal placeswhere possiblea. What is the distribution of X? X~ N(7.39b. What is the distribution of ? a~ N(]c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $7.7112and $8.2708d. For the group of 41 patrons, find the probability that the average lunch cost is between $7.7112 and $8.27082.94Yes ONoe. For part d), is the assumption that the distribution is normal necessary?Hint:

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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D, e, f and h
The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 60 minutes and a standard deviation of 14 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person at the hot springs stays longer then 81 minutes. c. The park service is considering offering a discount for the 7% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutes
he mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. What is the median giraffe height? ft.c. What is the Z-score for a giraffe that is 20 foot tall? d. What is the probability that a randomly selected giraffe will be shorter than 18.2 feet tall? e. What is the probability that a randomly selected giraffe will be between 18.9 and 19.6 feet tall? f. The 70th percentile for the height of giraffes is ft.
The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 64 minutes and a standard deviation of 14 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person at the hot springs stays longer then 57 minutes. c. The park service is considering offering a discount for the 7% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutes
Suppose it is known that the mean and standard deviation of the scores on a statistics final are 71.36 and 8.57, respectively. Calculate an interval that is symmetric around the mean such that it contains approximately 95% of scores. Assume that the scores have a normal distribution. Question 4 options: 1) (71.36, 8.57) 2) (54.22, 88.5) 3) (88.5, 54.22) 4) (62.79, 79.93) 5) (79.93, 62.79)
The average production cost for major movies is 57 million dollars and the standard deviation is 20 million dollars. Assume the production cost distribution is normal. Suppose that 46 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 57 20 b. What is the distribution of ? - N c. For a single randomly selected movie, find the probability that this movie's production cost is between 52 and 55 million dollars. 58 d. For the group of 46 movies, find the probability that the average production cost is between 52 and 55 million dollars. e. For part d), is the assumption of normal necessary? Yes No
Which of the following is True about the Z-score of an observation? A. The Z-score of an observation is defined as the number of standard deviations from the mean. B. If the observation is twice as large as the mean, its Z-score is 1. C. The Z-score of an observation is a number between 0 and 1. D. If the observation is right at the mean, its Z-score is 1.
Suppose the scores on an exam have a mean of 70 with a standard deviation of 10. If one student hasa test result with a z-score of -0.8 and a second student has a test result with a Z-score of 1.8, how many points higher was the second student's score than that of the first? O a. 10 O b. 20 O c. 2.6 O d. 13 O e. 26
Ex. 4. The mean and standard deviation of the marks obtained by 1000 students in an examination are respectively 34.5 and 16.5. Assuming the normality of the distribution, find the approxiamte number of students expected to obtain marks between 30 and 60.
Suppose baby kittens' weights are normally distributed with a mean of 10.7 and a standard deviation of 1.7. Find the baby kitten weight that corresponds to the following Z-scores. Round your answer to 3 decimals. a. Kitten a: Z = 0.75, weight b. Kitten b: Z = 1.92, weight c. Is Kitten a overweight, underweight, or exactly average? Exactly Average O Overweight Underweight d. Is Kitten b overweight, underweight, or exactly average? O Overweight O Underweight O Exactly Average
Find the standard deviation of workers with no drug problem from the sample. (Round your answer to the nearest hundredth)
The mean height of an adult giraffe is 17 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( b. What is the median giraffe height? ft. c. What is the Z-score for a giraffe that is 18.5 foot tall?

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