### Problem StatementA security guard knows that the time it takes to make the rounds in a certain warehouse is a random variable having a normal distribution with a mean of 18 minutes and a standard deviation of 3.2 minutes. What is the probability that the average time a sample of 64 security guards will take to complete the rounds of the warehouse is:#### (a) More than 17 minutes?#### (b) Between 17 and 18.9 minutes?### Explanation- **Mean (μ):** 18 minutes- **Standard Deviation (σ):** 3.2 minutes- **Sample Size (n):** 64 security guardsThis problem involves finding probabilities related to the sample mean of a normally distributed population. You can use the properties of the normal distribution and the concept of the standard error of the mean to solve these.

Given,mean(μ)=18standard deviation(σ)=3.2sample size(n)=64

Answered: #2 A security guard knows that the time…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

A study by the American Heart Association studied the distribution of birth weights for 1295 newborns (preterm babies excluded). They found that the birth weight of human babies is approximately normally distributed with a mean of 7.6 pounds and a standard deviation of 1.09 pounds. (a.) What is the probability that a randomly chosen baby weighs more than 9 pounds at birth? (b.) What is the probability that a randomly chosen baby weights between 6 and 8 pounds at birth? (c.) What is the 80th percentile for birth weight?
The SAT mathematics scores across the population of high school seniors are a normal random variable with a mean of 500 and a standard deviation of 100. Assume that the SAT mathematics test scores of different students are independent. (a) Find the probability that five randomly chosen seniors all score below 600. (b) What score must a student obtain to be in the 99th percentile?
The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 miles per gallon (mpg). If the standard deviation of the population was 2.8 and the gas ratings were normally distributed, (a) what is the probability that the mean mpg for a random sample of 25 light vehicles is under 18? (b) between 20 and 24?
Show neat and complete solution. (... The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 miles per gallon (mpg). If the standard deviation of the population was 2.8 and the gas ratings were normally distributed, (a) what is the probability that the mean mpg for a random sample of 25 light vehicles is under 18? (b) between 20 and 24? Given: Required: Solution: a. b.
In 2000, the average height of a woman aged 20-74 years was 64 inches with an increase of approximately 1 inch from 1960. Suppose the height of a woman is normally distributed with a standard deviation of two inches. • What is the probability that a randomly selected woman in this population is between 64 inches and 70 inches? • What is the probability that one woman selected at random from this population all exceed 70 inches? O a. NONE Ob.0.9973, 6.0042 x 10-9 Oc 0.0973, 0.0228 Od.0.4987, 0.0013
An automobile battery manufacturer claims that its mid grade battery has a mean life of 50 months with a standard deviation of 6 months Suppose the distribution of battery lives of this particular brand is approximately normal. Find the probability that the mean of a random sample of 36 such batteries will be less than 48 months. Is the assumption of the manufacturers' claims true? Why?
3
3
A machine produces small rods and large rods. The diameters of small rods are normally distributed with mean 2 cm and standard deviation 0.12 cm. The diameters of large rods are normally distributed with mean 2.2 cm and standard deviation 0.15 cm. (i) Find the probability that a randomly chosen small rod has diameter greater than 2.15 cm. (ii) A box contains one small rod and one large rod. Find the probability that at least one of the rods has diameter greater than 2.15 cm.
A supervisor at a local widget making company has been monitoring the output of one of the machines used to manufacture small aluminum plates. Past data indicate that if the machine is operating "properly," the length of the plates produced by this machine can be modeled as being normally distributed with a mean of 117 centimeters and a standard deviation of 5.2 centimeters. Suppose 16 plates produced by this machine are randomly selected. What is the probability that the average length of these 16 plates will be between 116 and 120 centimeters when the machine is operating "properly?" Z and t TABLES ARE GIVEN AS QUESTIONS 28-29. PLEASE SHOW ALL YOUR CALCULATIONS.CORRECT ANSWER WITHOUT CALCULATIONS WILL BE AWARDED PARTIAL CREDIT. Paragraph В I

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS