Search & Filtering
5. A fair die is rolled until a 6 occurs. Compute the probability that (a) 10 rolls are needed.
(b) an odd number of rolls is needed.
In a medical examination,300 people undergo a height measurement and was found out that the average height of all are 150 cm.
The continuous random variable x has the probability density function,
𝑓(𝑥) =
{
1/ 2(𝑥 - 2), 2 ≤ 𝑥 ≤ 3
𝑎, 3 < 𝑥 ≤ 5
2 - 𝑏𝑥, 5 < 𝑥 ≤ 6
0, 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
i. Find the values of a and b, and sketch the graph of f(x).
ii. Find the cumulative distribution function, f(x) and sketch it.
The continuous random variable x has the probability density function,
𝑓(𝑥) =
{
1/ 2(𝑥 - 2), 2 ≤ 𝑥 ≤ 3
𝑎, 3 < 𝑥 ≤ 5
2 - 𝑏𝑥, 5 < 𝑥 ≤ 6
0, 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
i. Find the values of a and b, and sketch the graph of f(x).
ii. Find the cumulative distribution function, f(x) and sketch it.
What is the probability that the height of a child, picked at random, is less than 104 cm?
What is the probability that the shelf life of the battery is between 400 days and 550 days?
7.The daily delivery of mail at a large city firm follows a time pattern conforming to the Normal
Distribution, with a mean time of arrival of 9.40 am and with a standard deviation of 20 minutes.
Estimate the number of occasions during the 250 working days in the year when the mail arrives
a. before the main gates open at 9 am
b. after the arrival of the office staff at 9.20 am
c. between 10 am and 10.20 am
A survey by Frank N.Magid Associates revealed that 3% of Americans are not connected to the Internet at home. Another researcher randomly selects 70 Americans.
a. What is the expected number of these who would not be connected to the Internet at home?
b. What is the probability that 8 or more are not connected to the Internet at home?
c. What is the probability that between 3 and 6 (inclusive) are not connected to the Internet at home?
Appendix A Statistical Tables
*(Round your answer to 1 decimal place.)
**(Round your answers to 4 decimal places when calculating using Table A.3.)
a. Expected number =
enter the expected number rounded to 1 decimal place
*
b. P(x ≥ 8) =
enter probability rounded to 4 decimal places
**
c. P(3 ≤ x ≤ 6) =
enter probability rounded to 4 decimal places
**
The Table A.3 is "Poisson Probability"
According to the Audit Bureau of Circulations, the top 25 city newspapers in the United States ranked according to circulation are:
Rank
Newspaper
1 New York Times (NY)
2 Los Angeles Times (CA)
3 New York Post (NY)
4 New York Daily News (NY)
5 Chicago Tribune (IL)
6 Washington Post (DC)
7 Las Vegas Review-Journal (NV)
8 Minneapolis Star Tribune (MN)
9 Denver Post (CO)
10 St. Petersburg Tampa Bay Times (FL)
11 Philadelphia Inquirer (PA)
12 Boston Globe (MA)
13 Dallas Morning News (TX)
14 Houston Chronicle (TX)
15 Austin American-Statesman (TX)
16 Newark Star-Ledger (NJ)
17 Phoenix Republic (AZ)
18 Springfield Republican (MA)
19 San Francisco Chronicle (CA)
20 Chicago Sun-Times (IL)
21 San Diego Union-Tribune (CA)
22 Seattle Times (WA)
23 Kansas City Star (MO)
24 Pittsburgh Post-Gazette (PA)
25 Sacramento Bee (CA)
Suppose a researcher wants to sample a portion of these newspapers and compare the sizes of the business sections of the Sunday papers. She randomly samples eight of these newspapers.
a. What is the probability that the sample contains exactly one newspaper located in New York state?
b. What is the probability that half of the sampled newspapers are ranked in the top 10 by circulation?
c. What is the probability that none of the newspapers is located in California?
d. What is the probability that exactly three of the newspapers are located in states that begin with the letter M?
(Round your answers to 4 decimal places.)
a. P(x = 1 in NY) =
enter probability rounded to 4 decimal places
b. P(x = 4 in top 10) =
enter probability rounded to 4 decimal places
c. P(x = 0 in California) =
enter probability rounded to 4 decimal places
d. P(x = 3 with M) =
enter probability rounded to 4 decimal places
A small scale restaurant owner wants to find an estimate of the average daily profit. For this, he randomly selected 25 days from the past year’s entry log and collected the following observations:
a. Sample mean of the daily profits for those 25 selected days = Rs. 33892
b. Sample standard deviation of the daily profits for those 25 selected days = Rs. 435
Assuming that daily profit values follow normal distribution, answer the following questions:
a) What is the target population? [1]
b) What is the population parameter that needs to be estimated? [1]
c) Find a 95% confidence interval for the population mean (average daily profit). [4]
d) How do you interpret this confidence interval obtained in 2.c)? [2]
e) Find a 95% confidence interval for the population mean (average daily profit) if the sample size is 100 instead of 25. [2]
