Search & Filtering
The time taken (in minutes) by all students in a class to complete a test follows a normal distribution of 57 with variance of 34. a) A student is randomly chosen from the class.
Find the probability that
i) he/she takes more than 52 minutes to complete the test. (4 marks)
ii) he/she takes between 41 to 76 minutes to complete the test. (4 marks)
b) 5 students are chosen from the class at random, find the probability that at most 3 of them takes less than 61 minutes to complete the test. (7 marks)
c) 12 students are chosen from the class at random, find the probability at all of them takes between 43 to 64 minutes to complete the test. (5 marks)
There are two AI (artificial intelligence) programs designed for a certain purpose, Kato and Goly. Both of them are run continuously and simultaneously to check for errors. It was found that the number of errors occur in an hour for Kato follows the Poisson Distribution with the mean of 4, whereas the number of errors occur in an hour for Goly follows the Poisson Distribution with the mean of 7.
Find the probability of the following, give your answer to at least 4 significant figures: a) exactly 3 errors occur in Kato within an hour. (3 marks)
b) at least 2 errors occur in Goly within an hour. (4 marks)
c) less than 6 errors occur in Kato within 3 hours. (5 marks)
d) more than 11 errors occur in Goly within 2.5 hours. (8 marks)
A box consists of 100 balls in total, for which 20 are red balls, 35 are blue balls, the rest are green balls. Moreover, each one of the 100 balls has either the letter “X” or “Y” printed on it. In total, 40 balls have letter “X” printed on them. Among the balls with “Y” printed on them, 26 are green and 14 are red.
d) If two balls are chosen at random, without replacement, find the probability that one of the balls is red and the other one is blue in color. (3 marks)
e) If two balls are chosen at random, without replacement, find the probability that exactly one ball is blue in color, and exactly one ball has the letter “X” printed on it (can be the same ball or different balls)
A word is to be formed using some or all of the 10 letters.
M A N C H E S T E R
Find the total number of ways of forming the word if
a) The word is 10-letter long. The letters can be in any combinations. (2 marks)
b) The word is 10-letter long. The word must begin with a consonant and end with a vowel. (5 marks)
c) The word is 2-letter long, and must not include T or E. (2 marks)
d) The word is 7-letter long. The word must contain at least one E. (6 marks)
e) The word is 5-letter long, no other restrictions. (5 marks)
Among 157 African-American men, the mean systolic blood pressure was 146 mm Hg with a standard deviation of 27. We wish to know if on the basis of these data, we may conclude that the mean systolic blood pressure for a population of African-American is 140
Suppose that X1, ... , Xn form a random sample from a distribution for the pdf f(x0) is as follows: 1 f(x|0) = - 1x-01 for 0 < x < 0 2 Also suppose that the value of 0 is unknown (-<< 0). Find the MLE of 0.
A teacher realizes that his students' marks on a statistic test are normally distributed with a mean of 62 and a standard deviation of 15. If the teacher wishes to assign minimum marks for grade B is referring to the top 30 per cent of the students' marks in the class, how many marks are required to get a minimum mark for grade B?
5.According to a local study, 80 per cent of workers in Malaysia work in an environment that could endanger their visual. If 20 Malaysia workers selected randomly as a sample, what is the probability
a) that exactly 16 workers work in such environment?
b) that more than 17 workers work in such environment?
c) that exactly 4 workers not work in such environment?
d) fewer than 3 workers the number not work in such environment?
A lottery will be conducted for the benefit of the poor but deserving students ata certain school. Four hundred tickets will be sold. One ticket will win P2000and the other tickets will win nothing. If you buy one ticket, what will be yourexpected value and variance of your gain.
Two coins are tossed. Let T be the number of tails that occur. Determine
the values of the random varable T
