COURSE DESCRIPTION
The ability to make sense of unstructured data, give meaning to certainty and uncertainty of occurrence, and determination of the way things change with time are obtain through the knowledge of statistics. Below are the topics to be covered:
- Theory of probability
- Measure of central tendency
- Normal distribution
- Geometric distribution
- Hypergeometric distribution
- Poisson distribution
- Sampling
- Chi-square distribution
- T- distribution
- Etc
Course Materials
Recommendably, we advise you to download Summaries and Textbooks (Probability & Statistics for Engineering and Sciences) related to this course.
Customers are used to evaluate preliminary product designs. In the past, 95% of highly successful product received good review, 60% of moderately successful products received good reviews, and 10% of poor products received good reviews. In addition, 40% of the products have been highly successful, 35% have been moderately successful, and 25% have been poor products.
- What is the probability that the product attains a good review?
- If a new design attains a good review, what is the probability that it will be a highly successful
- If a product does not attain a good review, what is the probability that it will be a highly successful product?
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Suppose your vehicle is licensed in a state that issues license plates that consist of three digits ( between 0 and 9) followed by three letters ( between A and Z). If a license number is selected randomly, what is the probability that yours is the one selected?
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Tutor:
Contamination is a problem in the manufacture of optical storage disks. The number of particles of contamination that occur on an optical disk has a Poisson distribution:
The average number of particles per centimeter squared of media surface is 0.1. The area of a disk under study is 100 squared centimeters
i. Find the probability that 4 particles occur in the area of a disk under study
ii. Determine the probability that 4 or fewer particle occur in the area of the disk under study
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Tutor: Aliyu Sulaiman
A random variable X has the exponential distribution:
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Suppose that X is a continuous random variable with probability distribution
F(x) = x/18 0<= x >= 6
Find the probability distribution of the random variable y = 2x + 10
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The probability that the head of a household is home when a telemarketing representative calls is 0.4. Given that the head of the house is home, the probability that goods will be bought from the company is 0.3. Find the probability that the head of the house is home and goods being bought from the company.
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Tutor: Aliyu Suleiman
An automobile manufacturer is concerned about a possible recall of its best-selling four-door sedan. If there were a recall, there is 0.25 probability that defect is in the break system, 0.18 in the transmission, 0.17 in the fuel system, and 0.40 in some other area.
a. What is the probability that the defect is the breaks or the fuelling system if the probability of defects in both systems simultaneously is 0.15?
b. What is the probability that there are no defects in either the breaks or the fuelling system
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Tutor: Aliyu Suleiman
Assignments
In the summary of the lecturer’s handout, there are some tutorial question which somewhere later converted to assignment base on the instruction below
INSTRUCTIONS
Answer the questions stated below from the summarized lecture given. Unless otherwise stated, all symbols carry their usual meanings.
Question: 7, 12, 17, 19, 36, 39, 42, 44, 46, 48, 49
Dowload EGR4201 Assignmet PDF HERE!
Download Complete Standard Distribution Table ↪
In an industrial process the diameter of a ball bearing is an important component part. The buyer sets specifications on the diameter to be 3.0 ± 0.01 cm. The implication is that no part falling outside these specifications will be accepted. It is known that in the process the diameter of a ball bearing has a normal distribution with mean p. = 3.0 and standard deviation a = 0.005. On the average, how many manufactured ball bearings will be scrapped?
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Tutor: Mustapha Tijjani Musa (SMB A.S.O)
Hospital administrators in large cities anguish about problems with traffic in emergency rooms in hospitals. For a particular hospital in a large city, the staff on hand cannot accommodate the patient traffic if there are more than 10 emergency cases in a given hour. It is assumed that patient arrival follows a Poisson process and historical data suggest that, on the average, 5 emergencies arrive per hour.
- a) What is the probability that in a given hour the staff can no longer accommodate the traffic?
- b) What is the probability that more than 20 emergencies arrive during a 3-hour shift of personnel?
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Tutor: Mustapha Tijjani Musa (SMB A.S.O)
The total number of hours, measured in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a continuous random variable X that has the density function
Find the probability that over the period of one year, a family runs their vacuum cleaner
- a) Less than 120 hours
- b) Between 50 and 100
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Tutor: Mustapha Tijjani Musa (SMB A.S.O)
In a certain city, the daily consumption of electric power, in millions of kilowatt-hours, is a
random variable X having a gamma distribution with mean 𝜇 = 6 and variance 𝜎2 = 12.
- a) Find the values of 𝛼 𝑎𝑛𝑑 𝛽.
- b) Find the probability that on any given day the daily power consumption will exceed 12 million kilowatt hours
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Tutor: Mustapha Tijjani Musa (SMB A.S.O)
An automobile manufacturer is concerned about a possible recall of its best-selling four-door sedan. If there were a recall, there is 0.25 probability that defect is in the break system, 0.18 in the transmission, 0.17 in the fuel system, and 0.40 in some other area.
- a. What is the probability that the defect is the breaks or the fuelling system if the probability of defects in both systems simultaneously is 0.15?
- b. What is the probability that there are no defects in either the breaks or the fuelling system
Watch Solution on YouTube: https://youtu.be/gHelMJ-5q8I
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Tutor: Mustapha Tijjani Musa (SMB A.S.O)
The probability that the head of a household is home when a telemarketing representative
calls is 0.4. Given that the head of the house is home, the probability that goods will be
bought from the company is 0.3. Find the probability that the head of the house is home and
goods being bought from the company.
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Tutor: Mustapha Tijjani Musa (SMB A.S.O)
A restaurant chef prepares a tossed salad containing, on average, 5 vegetables. Find the probability that the salad contains more than 5 vegetables
- a) On a given day
- b) On 3 of the next 4 days
- c) For the first time in April on April 5.
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Tutor: Mustapha Tijjani Musa (SMB A.S.O)
A truth serum has the property that 90% of the guilty suspects are properly judged while,
of course, 10% of guilty suspects are improperly found innocent. On the other hand,
innocent suspects are misjudged 1% of the time. If the suspect was selected from a group
of suspects of which only 5% have ever committed a crime, and the serum indicates that
he is guilty, what is the probability that he is innocent?
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Tutor: Mustapha Tijjani Musa (SMB A.S.O)
According to Chemical Engineering Progress (Nov. 1990), approximately 30% of all pipework failures in chemical plants are caused by operator error.
- a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error?
- b) What is the probability that no more than 4 out of 20 such failures are due to operator error?
- c) Suppose, for a particular plant, that, out of the random sample of 20 such failures, exactly 5 are operational errors. Do you feel that the 30% figure stated above applies to this plant? Comment.
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Tutor: Mustapha Tijjani Musa (SMB A.S.O)
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