Question
Do all work by hand Do NOT use a computer or a calculator that performs statistical calculations You must show your work in great detail for full credit with explanation on every important step. The following measurements represent the number of holes that a driling tool produces before it fails These tools are made in groups of 16 at a time. (a) Compute the following for the population: mean, median, mode, mean deviation, population standard deviation, population variance, and range. (b) Compute the sample standard deviation using the following tools:@ 1.4, lii) 5 (m) 912, and ()13-16 (c) Compute the maximum, the minimum, and the mean of the four sample standard deviations from (bl. What is the relative error for each sample standard deviationi.e.. il, i ), and (ill compared to the population standard deviation wo fair dice are relled. The absolute value of the difference of the outcomes is denoted by X For instance if one die gives 5, then x " 13-51#2) (a) What are the possible values of X and the probabilities associated with them? Find the mean and the mode. gives 3 and the other (c) Sketch a plot of the cumulative function F the probabilities of the evens below are as Probability of getting A on your final exam: 21% . Probability of getting B on your final exam: " probability of it raining on the test day: 52% . Probability that there will be a fire drill during the exam: 3% 2/2 The person sitting in front of you owns only four shirts of which one is green, one red, one blue and one yellow, and that the Probability that the person in front of you wi have on a green shirt: 18% Probability that the person in front of you wil have on a red shirt: 25% Probability that the person in front of you wi have on blue shirt: 22% Calculate the following probabilities in percent (a) Probablity of getting A or Bon the exäm (b) Probability of getting A on the exam and there being a fire drill and the person in front a you wearing a blue shint (c) Probability of getting CD, ar Fon the exanm the person in front of you having eithera blue or green shirt on and there being a fire drill on the exam. (d) Probability of it net raining on the test day and the person in front of you wearing a yellow shirt and you getting B on the exam A card is drawn at random from an ordinary desk of 52 playing cards. What is the probability that you obtain (a) A black king or a red jack? (b) A face card or a black card? ()Neither a clower nor a king?
Explanation / Answer
(A)
Probability of getting A or B = P(A or B) = 0.21 + 0.48 = 0.69
i.e. 69%
(B)
P(getting A) = 0.21
P(fire drill) = 3% = 0.03
P(blue shirt) = 22% = 0.22
P(getting A and fire drill and blue shirt) = 0.21 * 0.03 * 0.22 = 0.001386
i.e 0.1386%
(C)
P(getting C, D or F) = 1 - (0.21 + 0.48) = 0.31
P(blue or green shirt) = 0.18 + 0.22 = 0.4
P(fire drill) = 0.03
Required probability = 0.31 * 0.4 * 0.03 = 0.00372
i.e 0.372%
(D)
P(not raining) = 1 - 0.52 = 0.48
P(yellow shirt) = 1 - (0.18 + 0.25 + 0.22) = 0.35
P(getting B) = 0.48
Required probability = 0.48*0.35*0.48 = 0.08064
i.e. 8.064%
In all of the above problems we applied multiplication rule as all events are independent and mutually exlusive.
