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A plant has an effective capacity of 900 units per day and produces 800 units per day with its product mix. What is its efficiency?
Suppose the market has 70% chance of being favourable and 30% chance of being unfoavrable. A favourable market will yield a profit of N$300,000, while an unfavourable market will yield a profit of N$20,000. What is the expected monetary value in this situation?
Assume that random guesses are made for seven multiple choice questions on an SAT test, so that there are n=7 trials, each with probability of success (correct) given by p=.65 Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4 .
Let z be the random variable representing the number of blue balls. Find the values of the random variable Z.
A group of students got the following scores in an achievement test: 9, 12 15, 18, 21 and 24. Consider samples of size 3 can be drawn from this population.
B. Construct the sampling distribution of the resulting sample means
11. In the computing field, there are many applications of Probability theories. Hashing and Load Balancing are also included to those. Provide an example for an application of Probability in Hashing and an example for an application of Probability in Load Balancing. Then, evaluate in detail how Probability is used for each application while assessing the importance of using Probability to those applications.
11. The battery life of a certain battery is normally distributed with a mean of 90 days and a standard deviation of 3 days.
For each of the following questions, construct a normal distribution curve and provide the answer.
a) About what percent of the products last between 87 and 93 days?
b) About what percent of the products last 84 or less days?
For each of the following questions, use the standard normal table and provide the answer.
c) About what percent of the products last between 89 and 94 days?
d) About what percent of the products last 95 or more days?
The number of accidents in a production facility has a Poisson distribution with a mean of 2.7 per month. For a given month, what is the probability that there will be more than three (3) accidents?
Common Entrance are usually graded out of 150 marks. The education officers of one of the education districts, knows that the mean score in the district is 80 with a standard deviation of 20. The students’ scores follow a normal distribution. There are 500 students in the district who sat the Common Entrance Exam.
3) The education officer has promised to provide scholarships to the students in the district whose performance are in the top 1%.
i) What score separates the top 1% of students from the bottom 99% ?
ii)How many students are eligible to receive the scholarship?
If P(B) = 0.15, P(A | B) = 0.50, P(B′) = 0.85, and P(A | B′) = 0.60, find P(B | A)
