Suppose that the amount of time that students spendstudying in the library in one sitting is normally distributedwith mean 42 minutes and standard deviation 21 minutes. Aresearcher observed 45 students who entered the library tostudy. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X - N( 4221b. What is the distribution of x? x N 42~3.1305c. What is the distribution of Σæ? Σx - Nx? Xxd. If one randomly selected student is timed, find theprobability that this student's time will be between 38and 42 minutes.e. For the 45 students, find the probability that theiraverage time studying is between 38 and 42 minutes.f. Find the probability that the randomly selected 45students will have a total study time more than 1665minutes.g. For part e) and f), is the assumption of normalnecessary? No Yesh. The top 15% of the total study time for groups of 45students will be given a sticker that says "Greatdedication". What is the least total time that a groupcan study and still receive a sticker?minutes

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Answered: Suppose that the amount of time that…

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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Assume that adults have IQ scores that are normally distributed with a mean of u= 100 and a standard deviation g= 15. Find the probability that a randomly selected adult has an IQ less than 118. Click to view page 1 of the table. Click to view page 2 of the table. The probability that a randomly selected adult has an IQ less than 118 is (Type an integer or decimal rounded to four decimal places as needed.)
The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 70 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( 70 70 b. Find the probability that a randomly selected person at the hot springs stays longer then 69 minutes. c. The park service is considering offering a discount for the 8% 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? 46.115 X minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: 58.542 X minutes Q3: 81.458 X minutes IQR: 23.006 X minutes
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 259 feet and a standard deviation of 37 feet. Let X be the distance in feet for a fly ball.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly hit fly ball travels less than 243 feet. Round to 4 decimal places. c. Find the 90th percentile for the distribution of distance of fly balls. Round to 2 decimal places. feet
should be 4 decimal places
Suppose that the speed at which cars go on the freeway is normally distributed with mean 75 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,) b. If one car is randomly chosen, find the probability that it is traveling more than 72 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 76 and 80 mph. d. 78% of all cars travel at least how fast on the freeway? mph.
Assume that adults have IQ scores that are normally distributed with a mean of μ = 105 and a standard deviation o=20. Find the probability that a randomly selected adult has an IQ between 88 and 122. Click to view page 1 of the table. Click to view page 2 of the table. The probability that a randomly selected adult has an IQ between 88 and 122 is (Type an integer or decimal rounded to four decimal places as needed.) C
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.
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 268 feet and a standard deviation of 45 feet. Let X be the distance in feet for a fly ball.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly hit fly ball travels less than 338 feet. Round to 4 decimal places. c. Find the 90th percentile for the distribution of distance of fly balls. Round to 2 decimal places.  feet
he average amount of time boys and girls spend playing sports each week is believed to be the same. A sample of equal size n is taken from boys and girls , the mean of the boys is 29 hours with standard deviation 4 hours and the mean of the girls  is 27 hours with standard deviation 3 hours Both populations have a normal distribution. The calculated value is  1.2 n =
Suppose that the speed at which cars go on the freeway is normally distributed with mean 76 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. If one car is randomly chosen, find the probability that it is traveling more than 72 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 77 and 81 mph. d. 67% of all cars travel at least how fast on the freeway? mph.

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