Statistics and Probability Answers

a piece of equipment will function only when three components A,B and C are working. The probability of A failing during one year is 0.15, that of B is failing is 0.05 and that of C failing is 0.10. what is the probability that the equipment will fail before the end of the year?

A bag contain 5 white and 8 red balls. two drawings of 3 balls are made such that (a) the balls are replaced before the second trial and (b) the balls are not replaced before the second trial. Find the probability that the first drawing will give 3 white and the second, 3 red balls in each case

The following table shows the ages of people and the corresponding weight
Age(year) 25 40 38 53 40 32 48 59 45 36
Weight (Kgs) 43 52 48 61 63 40 67 72 47 41
Calculate the Spearman’s Rank correlation coefficient and comment.

The managing director of a company wants to find whether there is a relationship between units of a
product produces and the profits in a period of ten months
Month Jan Feb Mar Apr May June July Aug Sept Oct
Units produced (X)‘000 12 18 21 14 12 10 16 25 20 23
Profits (Y) ‘000 25 31 29 24 28 23 27 36 32 34
Calculate the regression equation of the form Y = a + bX and hence estimate the value of the profits when 12
units are produced. Clearly explain how this result compares to that given above as 28,000.

c) The table below shows the hours spent by ten men on a certain task and the units of an item produced.
Men A B C D E F G H I J
Hours (X) 16 14 15 18 20 15 19 21 12 24
Units
produced(Y)

28 24 27 33 31 33 34 36 21 40

Calculate and both the Pearson correlation coefficient and coefficient of determination, interpret both and
justify in this case why it would be prudent to rely on the coefficient of determination rather than Pearson in
decision making.

A college conducts both face to face and online classes that are intended to be identical. Given below are
the distributions of the two groups in terms of marks scored in a statistics examination.
Face to face Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70
No. of Students 5 10 20 25 15 15 10
On-line Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70
No. of Students 10 25 30 40 30 20 15
Test the hypothesis that the mean marks are statistically equal at the 5% level of significance and write a 5%
confidence interval estimate of the difference

A project company hired 800 casual employees to undertake a task for 1 week. On average (daily)
these workers take 10 hours to complete the task with a s.d deviation of 2 hours. If completion time is
normally distributed, determine the no. of workers who completed the task in:-
i. Less than 8 hours
ii. Less than 12.5 hours
iii. More than 13.5 hours
iv. Between 7.5 hours and 14 hours
v. Between 6.2 hours and 10 hours
vi. If the firm decides to lay off all the workers who cannot complete the task within hours, how
many workers will the firm lay-off?

Suppose that a market research rm is hired to estimate the percent of adults living in a large city who have cell phones. 500 randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes –they own cell phones. 3.1)Using a 90% confidence level, compute a confidence interval estimate for the true proportion of adults residents of this city who have cell phones.(6)3.2)Using a 99% confidence level, compute a confidence interval estimate for the true proportion of adults residents of this city who have cell phones.(4)3.3)Comment on the findings between questions 3.1 & 3.

Suppose x is distributed with a mean of 25.1 and a standard deviation of 3.2. What is the probability of randomly selecting an individual from the distribution with value that is greater than 21.2 and less than 23.4