Question
In: Statistics and Probability
Every day there is a random number of pencils in the mail. Jerry places eraser caps...
Every day there is a random number of pencils in the mail. Jerry places eraser caps on each one that arrives. Jerry has enough eraser caps to cap 600 pencils. Each day, Jerry gets at least two pencils, but not more than a dozen, and he always receives an even number of pencils. Among the possible numbers of pencils Jerry might receive, all are equally likely. Moreover, different days are independent. What is the approximate probability that Jerry's amount of eraser caps will last at least three months? Assume there are 30 days in every month.
Solutions
Expert Solution
Use central limit theorem to approximate the probability of the total number of pencil bought in 30 days being less than or equal to 600.
Central Limit Theorem
Multipyling numerator and denominator of the LHS by n, we get this version of the Central Limit Theorem
Also use additivity of expectation and result for variance of
sums to find the mean and variance of 
to substitute in the central limit theorem.
Note:
orchestra answered 2 years agoRelated Solutions
I'm generating a random number every 10 second; In arraylist I'm Storing and Updating the number...
I'm generating a random number every 10 second; In arraylist I'm
Storing and Updating the number every 10 second when I generate new
number. However, my goal to call the update number from arraylist
in another class main method. I would apperciate any help.
//this is the class I'm generating a random number every 10
second and Storing and Updating the number in arraylist.
package com.singltondesignpattern;
import java.util.ArrayList;
import java.util.Random;
import java.util.concurrent.Executors;
import java.util.concurrent.ScheduledExecutorService;
import java.util.concurrent.TimeUnit;
public class EverySecond {...
A telephone company claims the average number of phone calls made every day in a household...
A
telephone company claims the average number of phone calls made
every day in a household is more than three. A random sample of 169
days is survey in a mean of two and a standard deviation of .2 are
found, test the claim at a 5% level of significance. Assume the
district distribution is normal.
What's new about Covid-19 this month? Is the number of patients decreasing every day or not?...
What's new about Covid-19 this month? Is the number of patients
decreasing every day or not? Brief literature review with
reference
Western Airlines merged with a smaller airline recently. Every day since the merger, a random sample...
Western Airlines merged with a smaller airline recently. Every
day since the merger, a random sample of 30 Western flights has
been analyzed. A flight that takes off more than 10 minutes after
its scheduled departure time is considered to be late; otherwise,
it is not late. Western’s performance over the past 10 days is
shown in the table below.
Day 1 2 3 4 5 6 7 8 9 10 # Late Flights 4 2 5 9 2 3...
Western Airlines merged with a smaller airline recently. Every day since the merger, a random sample...
Western Airlines merged with a smaller airline recently.
Every day since the merger, a random sample of 30 Western flights
has been analyzed. A flight that takes off more than 10 minutes
after its scheduled departure time is considered to be late;
otherwise, it is not late. Western’s performance over the past 10
days is shown in the table below.
Day
1 2 3 4 5 6 7 8 9 10
# Late Flights 4 2 5 9 2 3...
3. Below is the number of texts per day for a random sample of students from...
3. Below is the number of texts per day for a random sample of
students from last semester. (Population normal enough.)
a. Create the 95% confidence interval for both sets of data. Is
there evidence that the population means are different? Under 19
years old: 250, 15, 200, 10, 15, 50, 20, 150, 63, 15, 7, 20, 35, 4,
20 At least 19 years old: 100, 20, 40, 5, 30, 100, 100, 65, 5, 25,
20, 50, 10, 10
b....
The number of computers sold during one day by a small store is a random variable...
The number of computers sold during one day by a small store is
a random variable XX with the following distribution:
P(0)=0.12,P(1)=0.19,P(2)=0.19,P(3)=0.12,P(4)=0.06,P(5)=0.32P(0)=0.12,P(1)=0.19,P(2)=0.19,P(3)=0.12,P(4)=0.06,P(5)=0.32
a. Compute the expected value E(X)E(X). Give your answer two
decimal places.
E(X)=E(X)=
b. Compute the standard deviation σ(X)σ(X). Give your answer two
decimal places.
σ(X)=σ(X)=
1 point) The problem below describes an experiment and defines a
random variable.
(a) Find the distribution of the random variable (and provide it as
a chart).
(b) Calculate the expected value...
<< Using R code >> Set seed number as "12345" every time you generate random numbers....
<< Using R code >>
Set seed number as "12345" every time you generate random
numbers. For each answer,
use # to explain if necessary.
2) Generate a data.frame "D" with 3 variables.
The 1st variable "v1" has 50 number of N(5,3^2) (normal with mean
5, standard deviation 3)
The 2nd variable "v2" has 50 number of exp(5) (exponential with
parameter 5)
The 3rd variable "v3" has 50 random characters from lower case
alphabets.
2-1) Rename the variable from "v1",...
If you played the same four-digit number every day (or any four-digit number for that matter) in the Big 4, how often (in years) would you win, assuming you have average luck?
If you played the same four-digit number every day (or any four-digit number for that matter) in the Big 4, how often (in years) would you win, assuming you have average luck?
The trade volume of a stock is the number of shares traded on a given day. The given data file contains the volume(in millions) of PepsiCo stock for a random sample of 40 trading days.
Volume (in millions)
2.37
2.42
3.25
3.94
4
4.02
4.13
4.16
4.28
4.35
4.41
4.42
4.64
4.8
4.84
4.92
4.95
4.97
4.98
5.04
5.05
5.07
5.32
5.55
6.1
6.16
6.22
6.23
6.39
6.67
6.69
6.71
6.92
6.96
7.28
7.29
7.54
7.56
7.71
8.88
The trade volume of a stock is the number of shares traded on a given day. The given data file contains the volume(in millions) of PepsiCo stock for a random sample of 40 trading days.
(1) Use...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Each player throws both dice once per turn. The player only scores when the player throws...
- If water is seeping, the effective stress at any point in a soil mass will be...
- QUESTION 2 [35 MARKS] Consider the following information of Petronas Bond Description Petronas Bond Face value...
- Do relativism and subjectivism generate contradictions? Why might someone accuse the theories of doing so? How...
- Analyze the industry environment of Walmart in 2018
- 1. In the following ordinary annuity, the interest is compounded with each payment, and the payment...
- The Lost Continent Store pays a constant dividend. Last year, the dividend yield was 5.75 percent...
ADVERTISEMENT