Statistics and Probability Answers

a test has been given for many years with mean score 60 and standard deviation 8. a group of 50 students were selected and gives a special training. these 50 students obtained average score of 65. can we say that special training has changed the score? use alpha as 0.05.

in a sample survey 6 estimates were made of the same mean when population mean become known. the following error were computed -35,111,-88,47,-12 and 26. are these errors consists with a hypothesis that population of error has zero mean?

The probability that a student passes a Physics test is (2/3) and the probability that he passes both Physics and English test is (14/45). The probability that he passes at least one test is (4/5). What is the probability that the student passes the English test?

If two dice are thrown what is the probability that the sum is
(1)greater than 8
(2)neither 7 nor 11

Proof Boole's inequality
for n events A1,A2,...An.

Five salesman A, B, C, D and E of a company are considered for a three member trade
delegation to represent the company in an international trade conference. Construct the sample
space and find the probability that (i) A is selected (ii)A is not selected (iii) Either A or B (not both) is selected.

Which one of the following statements is correct?
(1) Fake news post count is a qualitative nominal variable.
(2) Fake news post count is a categorical variable measured on an ordinal scale.
(3) Fake news post count is a quantitative discrete variable.
(4) Fake news post count is a quantitative continuous variable measured on a ratio.
(5) None of the above.

Wanda and her sister, Siyabulela entered a lucky draw and can win R250 000 worth of prizes
from a gaming magazine. Wanda sent through 15 entry forms, while Siyabulela sent through 35.
The report from the competition administrators is that 400 entries qualified, and both Wanda and
Siyabulela qualified. Use this information to answer the following questions:
1.1 What is the probability that Wanda will win first prize?

Consider a random group of kpeople who tested positive for COVID-19. Their birthdays have been written down for statistical purposes regarding COVID-19 control measures.
a.Determine the least k such that it is more likely than not that two people or more have the same birthday.
b.Determine the smallest k such that it is more likely than not that two or more people share your birthday.