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What does pr mean for coin?
PR is a grading system used for proof coins
What is the 68-95-99.7 rule and could you demonstrate on these problems the mean of 70 and a standard deviation of 15 less than 55 less than 40 less than 85 less than 100 greater than 85?
The rule applies to the normal distribution. For any normal distribution, 68% of the observations lie within 1 standard deviation (SD) either side of the mean that is, between (mean - SD) and (mean + SD); 95% of the observations lie between (mean - 2*SD) and (mean + 2*SD); 99.7% between (mean - 3*SD) and (mean + 3*SD). To find the probability that a normally distributed random variable, with mean = m and SD = s, you calculate its z-score = (X - m)/s and look up the relevant probability value in tables. In doing this, you may have to use the symmetry of the normal distribution or the probability of complementary events (or both). This will depend on what exactly is tabulated. Mean 70, SD = 15 Pr[X < 55] = Pr[Z < (55 - 70)/15] = Pr[Z < -1] = 0.5*(1-0.68) = 0.5*0.32 = 0.16 Pr[X < 40] = Pr[Z < (40 - 70)/15] = Pr[Z < -2] = 0.5*(1-0.95) = 0.5*0.05 = 0.025 Pr[X < 85] = Pr[Z < (85 - 70)/15] = Pr[Z < 1] = 1 - 0.16 = 0.84 Pr[X < 100] = Pr[Z < (100 - 70)/15] = Pr[Z < 2] = 1 - 0.025 = 0.975 Pr[X > 85] = 1 - Pr[X < 85] = 1 - 0.84 = 0.16
What is the describing of the complementary event and find its probability?
Suppose there is an event A and the probability of A happening is Pr(A). Then the complementary event is that A does not happen or that "not-A" happens: this is often denoted by A'.Then Pr(A') = 1 - Pr(A).Suppose there is an event A and the probability of A happening is Pr(A). Then the complementary event is that A does not happen or that "not-A" happens: this is often denoted by A'.Then Pr(A') = 1 - Pr(A).Suppose there is an event A and the probability of A happening is Pr(A). Then the complementary event is that A does not happen or that "not-A" happens: this is often denoted by A'.Then Pr(A') = 1 - Pr(A).Suppose there is an event A and the probability of A happening is Pr(A). Then the complementary event is that A does not happen or that "not-A" happens: this is often denoted by A'.Then Pr(A') = 1 - Pr(A).
What is the difference between the multiplication rule for independent versus dependent events?
Given two events, A and B, Pr(A and B) = Pr(A)*Pr(B) if A and B are independent and Pr(A and B) = Pr(A | B)*Pr(B) if they are not.
What is the probability of obtaining exactly three heads in four flips of a coin given that at least two are heads?
Pr(3H given >= 2H) = Pr(3H and >= 2H)/Pr(>=2H) = Pr(3H)/Pr(>=2H) = (1/4)/(11/16) = 4/11.
