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g) What is the probability that 190 < X < 205? h) What is the probability that Xtot >16300 minutes?

g) What is the probability that 190 < X < 205? h) What is the probability that Xtot >16300 minutes?

A First Course in Probability (10th Edition)
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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The time needed for a random student to complete Quiz #3 in Mat 301 has approximately a normal distribution with mean = 197.1 minutes and a standard deviation of σ= 20.7 minutes. Suppose that the class has n=81 students and every student takes the quiz. Let X be the random variable representing the mean time (in minutes) that the 81 students needed to complete the quiz. Let Xtot be the random variable representing the total time in minutes that the 81 students needed to complete the quiz. a) About what proportion of students in Mat 301 take between 195 and 205 minutes to complete the exam? b) About what proportion of students in Mat 301 take more than 230 minutes to complete the quiz? c) About how many of the 81 students took more than 230 minutes to complete the quiz? (nearest integer) d) About how many of the 81 students took between 195 and 205 minutes to complete the quiz?(nearest integer)? e) What is the standard deviation of the distribution of X (in minutes)? f) What is the standard deviation of the distribution of Xtot (in minutes)? g) What is the probability that 190 < X < 205? h) What is the probability that Xtot > 16300 minutes? f) Copy your R script for the above into the text box here.
Transcribed Image Text:The time needed for a random student to complete Quiz #3 in Mat 301 has approximately a normal distribution with mean = 197.1 minutes and a standard deviation of σ= 20.7 minutes. Suppose that the class has n=81 students and every student takes the quiz. Let X be the random variable representing the mean time (in minutes) that the 81 students needed to complete the quiz. Let Xtot be the random variable representing the total time in minutes that the 81 students needed to complete the quiz. a) About what proportion of students in Mat 301 take between 195 and 205 minutes to complete the exam? b) About what proportion of students in Mat 301 take more than 230 minutes to complete the quiz? c) About how many of the 81 students took more than 230 minutes to complete the quiz? (nearest integer) d) About how many of the 81 students took between 195 and 205 minutes to complete the quiz?(nearest integer)? e) What is the standard deviation of the distribution of X (in minutes)? f) What is the standard deviation of the distribution of Xtot (in minutes)? g) What is the probability that 190 < X < 205? h) What is the probability that Xtot > 16300 minutes? f) Copy your R script for the above into the text box here.
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