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Sheet 1
A study of 200 computer services firms revealed these incomes after taxes:
Income After Taxes Number of Firms Under $1 million 102 $1 million up to $20 million 61 $20 million and more 37
What is the probability that a particular firm selected has $1 million or more in income after taxes?
Routine physical examinations are conducted annually as part of a health service program. It was discovered that 8% of the employees needed corrective shoes, 15% needed major dental work and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work?
A survey of top executives revealed that 35% of them regularly read Time magazine, 20% read Newsweek and 40% read U.S. News & World Report. Ten percent read both Time and U.S. News & World Report. What is the probability that a particular top executive reads either Time or U.S. News & World Report regularly?
There are 10 rolls of film in box and 3 are defective. 2 rolls are to be selected without replacement. What is the probability of selecting a defective roll followed by another defective roll?
Giorgio offers the person who purchases an 8 ounce of Allure twee free gifts, either an umbrella, a 1 ounce bottle of Midnight, a feminine shaving kit, a raincoat or a pair of rain boots. If you purchased Allure what is the probability you selected at random an umbrella and a shaving kit in that order?
A board of directors consists of 8 men and 4 women. A four-member search committee is to be chosen at random to recommend a new company president. What is the probability that all 4 members of the search committee will be women
A1A2SumB13070100B2100150250B36040100B4104050Sum 200300500
Compute:
P(B1/A2)
P(B3/A1)
P(B4/A2)
P(B2/A2)
DEM 508
Sheet 2
Judging from recent experience, 5 percent of the computer keyboards produced by an automatic, high-speed machine are detective. What is the probability that out of six keyboards selected at random, exactly zero keyboards will be detective?
Sixty percent of the customers of a fast food chain order the whopper, french fries and a drink. If a random sample of 15 register receipts is selected, what is he probability that 10 or more will show that the above three food items were ordered?
On a very hot summer day, 5 percent of the production employees at midland states steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism. What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?
An insurance agent has appointments with four prospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is 1 out of 5. Using the rules of probability, what is the likelihood that the agent will sell a policy to 3 of the 4 prospective clients?
A true-false test consists of six questions. If you guess the answer to each question, what is the probability of getting all six questions correct?
DEM 508
Sheet 3
A board of directors consists of 8 men and 4 women. A four-member search committee is to be chosen at random to recommend a new company president. What is the probability that all 4 members of the search committee will be women
Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.0005. Suppose they wrote 400 policies for the coming weekend, what is the probability that exactly two claims will be filed?
There are 10 rolls of film in box and 3 are defective. 2 rolls are to be selected without replacement. What is the probability of selecting a defective roll followed by another defective roll?
There are 50 photos in a book which has 250 pages. Find the probability that page 100 has no photo.
Suppose the average number of lions seen on a 1-day safari is 5. What is the probability that tourists will see fewer than four lions on the next 1-day safari?
The department of statistics has 12 staff members. 8 of them are under 60 years old. If we want to establish a committee of 4 memebers:
What is the probability that all members of the committee are over 60 years old?
What is the probability that the committee has only 2 members are over 60 years old?
What is the probability that at least one member is not over 6o years old?
In a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?
DEM 508
Sheet 4
The mean amount spent by a family of 4 on food per month is $500 with a standard deviation of $75. Assuming that the food costs are normally distributed, what is the probability that a family spends less than $ 410 per month?
What is the proportion of the total area under the normal curve within plus and minus two standard deviation of the mean?
The mean score of a college entrance test is 500; the standard deviation is 75. The score are normally distributed. What percent of the students scored below 320?
A new car was put into production. It involved many assembly tasks. Each car was inspected at the end of the assembly line and the number of defects per unit was recorded. For the first 100 cars produced, there were 40 defective cars. Some of the cars had no defects; a few had one defect, and so on. The distribution of defects followed a Poisson distribution. Based on the first 100 produced, about how many out of every 1,000 cars assembled should have one or more defects?
The mean of a normally distributed group of weekly incomes of a large group of executives is $1000 and the standard deviation is $100. What is the z-score for an income of $1100?
A study of a companys practice regarding the payments of invoices revealed that an invoice was paid an average of 20 days after it was received. The standard deviation equaled five days. Assuming that the distribution is normal, what percent of the invoices were paid within 15 days of receipt?
DEM 508
Sheet 5
1- A life insurance salesman sells on the average 3 life insurance policies per week. Use Poisson's law to calculate the probability that in a given week he will sell
some policies
2 or more policies but less than 5 policies.
Assuming that there are 5 working days per week, what is the probability that in a given day he will sell one policy?
2- It was found that the mean length of 100 parts produced by a lathe was 20.05 mm with a standard deviation of 0.02 mm. Find the probability that a part selected at random would have a length
between 20.03 mm and 20.08 mm
between 20.06 mm and 20.07 mm
less than 20.01 mm
greater than 20.09 mm.
3 -The average life of a certain type of motor is 10 years, with a standard deviation of 2 years. If the manufacturer is willing to replace only 3% of the motors that fail, how long a guarantee should he offer? Assume that the lives of the motors follow a normal distribution.
4 -Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?
5-A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of
more than 2 hits?
at least 3 misses?
6- Vehicles pass through a junction on a busy road at an average rate of 300 per hour.
Find the probability that none passes in a given minute.
Find the probability that at most two passes in a given minute.
7-A tennis match requires that a player win three of five sets to win the match. If a player wins the first two sets, what is the probability that the player wins the match, assuming that each player is equally likely to win each match?
8- 15 states with the largest population and 10 of them do not have any coastline. Suppose 3 states are selected at random
What is the probability that none of the states selected have any coastline
What is the probability that exactly one state has coastline
What is the probability that at least one has coastline
Compute mean and standard deviation
9- Suppose that a shipment contains 5 defective items and 10 non defective items .If 7 items are selected at random without replacement
what is the probability that all items are good?
What is the probability that exactly 2 items are defective?
what is the probability that at most 4 good items will be obtained?
Compute the mean and the standard deviation
10- suppose the probability of success for Amr is 3/5 and probability of fail for Ali is 1/3. Find the following probabilities
Amr will not success
Ali will success
Amr and Ali together will success
At least one of them will success
Amr will success and Amr will not
Neither one will success
11-
A1A2SumB18070150B2120150270B39040130B411040150Sum 400300700
Compute:
P(B1/A2)
P(B3 and A1)
P(B4 and A2)
P(B2/A2)
P(B2 and A1)
DEM 508
Sheet 6
1- Uniform: The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between 0 and 15 minutes, inclusive.
What is the probability that a person waits fewer than 12.5 minutes?
On the average, how long must a person wait?
Find the standard deviation, .
How many minutes the person must wait if he wait for ninety percent of the time?
2- The number of donuts a nine-year old child eats per month is uniformly distributed from 0.5 to 4 donuts, inclusive.
Find the probability that a randomly selected nine-year old child eats more than two donuts
Find the probability that a different nine-year old child more than two donuts given that his or her amount is more than 1.5 donuts.
3- A company pays its employees an average wage of $3.25 an hour with a standard deviation of 60 cents. If the wages are approximately normally distributed, determine
the proportion of the workers getting wages between $2.75 and $3.69 an hour;
the minimum wage of the highest 5%
4- An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before they fail is 19.0 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.2 hours. About 95.44 percent of the batteries failed between what two values?
DEM 508
Sheet 7
The wildlife department has been feeding a special food to rainbow without trout fingerlings in a pond. A sample of the weights of 40 trout revealed that the mean weight is 402.7 grams and the standard deviation 8.8 grams. What is the probability that the mean for a sample of 40 trout exceeds 405.5 grams?
Suppose a search firm conducted a survey to determine the average amount of money steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $20 and the sample standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21?
The mean weight of trucks traveling on a particular section of I-475 is not known. A sate highway inspector needs an estimate of the mean. He selected a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 4.2 tons. What is the probability that a truck will weigh less than 14.3 tons?
There are 2000 eligible voters in a precinct. 500 of the voters are selected at random and asked to indicate whether they planned to vote for the democratic incumbent or the Republican challenger. Of the 500 surveyed, 350 said they were going to vote for the Democratic incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote the Democratic incumbent?
A random sample of 85 group leader, supervisors, and similar personnel revealed that a person spent an average 6.5 years on the job before being promoted. The population standard deviation was 1.7 years. Using the 0.95 degree of confidence, what is the confidence interval for the population mean?
Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread life was found to be 50,000 miles with a standard deviation of 3,500 miles. What is the best estimate of the average tread life in miles for the entire population of these tires?
DEM 508
Sheet 8
Students scores are normally distributed with mean = 65 and standard deviation = 10. If we select a random sample of 25 students, the scores mean of this sample will be 55. at = 0.05 can we conclude that:
The scores mean is different than 65
The scores mean is grater than 65
A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these self lives (in days); 215, 217, 218, 219, 216, 217, 217, 218 and 218. At the 0.0025 level, has the shelf life of the cake mix increased?
A manufacturer wants to increase the absorption capacity of sponge. Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume that a two tailed test at 0.10 significance level is to be used. For what value of t will the null hypothesis be rejected?
The claim that 40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available is to be investigated at the 0.02 level of risk. If 74 out of the 200 workers sampled said they would return to work, what is our decision?
DEM 508
Sheet 9
A course in mathematics is taught to 12 students by the traditional classroom procedure. A second group of 10 students was given the same course by means of programmed materials. At the end of the semester the same examination was given to each group. The 12 students meeting in the classroom made an average grade of 85. While the 10 students using programmed materials made an average of 81. Assume the populations to be approximately normal with standard deviations of 4 and 5 respectively. At 0.1 level of significance:
a - Is there a significant difference between the two learning method?
b - Do the students using programmed materials make a better average that the students meeting in the classroom?
c Do the students meeting in the classroom make a better average that the students using programmed materials?
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