Search & Filtering
a) Mzee Kobe Bank wished to establish the times in seconds that each ATM transaction takes. A sample of ATM users were observed and the time in seconds each spent at the ATM was as follows:
Time (seconds)
10-19
20-29
30-39
40-49
50-59
Number of customer
15
60
67
98
2
i.Calculate the coefficent of variation of the waiting time? ( 6 marks)
Consider a new card game between 2 players: Darryl (player 1) and Phyllis (player 2)
Darryl is dealt two cards : ♡6 and ♠5 . Phyllis is also dealt two cards: ♢3 and ♣9 . Now, each of the players will play 1 card both at the same time.
The payoff of Darryl is 1 points if he plays a card of opposite color (red/black) than Phyllis, and otherwise his payoff is 6 points.
The payoff of Phyllis is 9 points if the difference of the already played card numbers is greater than 5, otherwise her payoff is 1 points.
Find the action sets of each player and the action profile of the game.
Represent the game in the Normal form.
Find the Best Responses for Darryl.
Find the Best Responses for Phyllis.
Find all the Nash Equilibriums of the game (if any)
Count the number of heads in each outcomes and assign this number to this outcomes.
Solve. Given a population of the scores of BSHS honor students in Mathematics as 1, 3, 4, 6, and 8. Suppose a sample size of 3 have to be drawn from it for the first, second and third rank;
1. The mean inside diameter of a sample of 200 washers produced by a machine is 0.502 inch and the standard deviation is 0.005 inch. The purpose for which these washers are intended allows a maximum tolerance in the diameter of 0.496 to 0.508 inch, otherwise, the washers are considered defective. Determine the percentage of defective washers produced by the machine, assuming that the diameters are normally distributed.
The standard deviation of the running time of a sample of 200 fuses was found to be 110 hours. Find a 99% confidence interval for the standard deviation of all such fuses.
The standard deviation of the running time of a sample of 200 fuses was found to be
100 hours. Find a 99% confidence interval for the standard deviation of all such fuses.
Question
Q4
In a random sample of 400 students and 600 graduates who studies a given pre-
requisite course upon entry into university, 100 students and 300 graduates indicated
that they found it helpful. Construct a 99% confidence interval for the difference in
proportions of all students and all graduates who took a given pre-requisite course and
found it helpful.
b) The standard deviation of the running time of a sample of 200 fuses was found to be
100 hours. Find a 99% confidence interval for the standard deviation of all such fuses.
c) Two samples, sample one of size 16 and sample two of size 10, respectively, are drawn
at random from two populations that are normally distributed. If their variances are
found to be 24 and 18, respectively, find:
i. 98% confidence interval for the ratio of the variances.
ii. 90% confidence interval for the ratio of the variances.
Let x be a continuous random variable having density function fx(x)= 1/2 e^-|x| dx, - infinity< x<infinity. show that Mx(t)= (1-t^2)^-1 , -1<x<1
Suppose a study conducted on where people turn for news was based on 400 respondents. Of the
400 respondents, 199 got their news primarily from newspapers.
(a) Calculate the point estimate and standard error of the proportion of people who get their news
primarily from newspapers.
(b) Is there evidence that the proportion of people who get their news primarily from newspapers
is 0.5 or more? (use 𝛼 = 0.01)
(c) Determine the 𝑝-value in (b).
(d) Construct a 99% confidence interval estimate of the true population proportion of respondents
who get their news primarily from newspapers.
