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=81students 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 timein 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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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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SAT scores in one state is normally distributed with a mean of 1487 and a standard deviation of 104. Suppose we randomly pick 59 SAT scores from that state. a) Find the probability that one of the scores in the sample is greater than 1480.
Assume that adults have IQ scores that are normally distributed with a mean of mu = 100 and a standard deviation sigma = 20. Find the probability that a randomly selected adult has an IQ between 84 and 116 and type an integer or decimal rounded to four decimal places. Make sure to use the positive or negative z score charts attached, in the eBook on MSL, or in a hardcopy of the textbook.
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The lengths of home runs hit by players for the Mets have approximately a normal distribution with μ = 399 feet and a standard deviation of σ=31.16 feet. Suppose that we randomly select 81 home runs hit by players of the Mets. Let X be the random variable representing the mean length of home runs in feet and let Xtot be the random variable representing the sum of the lengths of the home runs in feet for the 81 selected home runs. d) About how many of the 81 sampled home runs have length between 400 and 420 feet? (nearest integer) e) What is the standard deviation of the distribution of X? f) What is the standard deviation of the distribution of Xtot?
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The weight of a male bald eagle has approximately a normal distribution with mean ?= 7.4 pounds and a standard deviation of ?= 1.6 pounds. Suppose we take a random sample of n=64 male bald eagles. Let X̄ be the random variable representing the mean weight in pounds of the 64 sampled male bald eagles. Let Xtot be the random variable representing sum of the weights of the 84 sampled bald eagles. a) About what proportion of male bald eagles have weights between 7.0 and 7.8 pounds? b) About what proportion of male bald eagles have weights greater than 7.8 pounds? c) About how many of the 64 sampled male bald eagles would you expect to have weight greater than 7.8 pounds? (nearest integer)? d) About how many of the 64 sampled male bald eagles would you expect to have weight between 7.0 and 7.8 pounds? (nearest integer)? e) What is the standard deviation of the distribution of X̄ (in pounds)? f) What is the standard deviation of the distribution of Xtot (in pounds)? g) What is the…
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