3. Here we find a z-score that corresponds to a given percentile (a)* Find the z-score that marks the 85th percentile (denoted Pas). That is, find the z-score that delineates the lower 85% from the upper 15% of all the z-scores. (b) Find the z-score that marks the 25th percentile (denoted P25). That is, find the z-score that delineates the lower 25% from the upper 75% of all the z-scores.2. The Poisson distribution describes the probability to observe 3 events during a certain measurement interval, given a mean rate a: :1: Ppimlvi = \"e-r Note that a: has to be a positive integer. {3} ('3') [o] Plot {on a single panel} the Poisson distribution for rates of a: = l, 2, 4, 1|]. [CU Show that. the mean of the Poisson distribution is a. 1 Show that. the variance of the Poisson distribution is pt. For p. 2 3E}, plot the Poisson distribution, as well as a Gaussian distribution of mean a = 313. Motivate your choice of standard deviation when plotting the Gaussian. 3.24 Negative binomial and Poisson distribution. Show that the negative binomial distribution of the form (3.109) approaches the Poisson distribution with mean A if we let r > 00 and (1 p) > 0 in such a manner that (1 p)r = l. Hint: r 1n(1/p) also converges to A. Average SD Party Hours 12 11 Number of Drinks 8 9 Correlation: r = 0.5 1. Drink Z score Number of Drinks Per Week Party Hours Per Week Party Z score (Don't round z scores) r=0.5 (Don't round z scores) (Don't round) 23 r=0.5 Submit Answer | Tries 0/3 2. Party Hours Per Week Party Z score (Don't round z scores) r=0.5 Drink Z score Number of Drinks Per Week (Don't round z scores) (Don't round) 1 r=0.5 Submit Answer | Tries 0/3 3 Party Hours Per Week Party Z score r=0.5 Drink Z score Number of Drinks Per Week (Don't round z scores) (Don't round z scores) (Don't round) 12 r=0.5 Submit Answer Tries 0/3 4 Party Hours Per Week Party Z score r=0.5 Drink Z score Number of Drinks Per Week (Don't round z scores) (Don't round z scores) (Don't round) 34 r=0.5 Submit Answer Tries 0/3 5 Party Hours Per Week Party Z score Drink Z score Number of Drinks Per Week (Don't round z scores) =0.5 (Don't round z scores) (Don't round) (Don't Round your answer. (Hint:Not the same answer as above!) =0.5 17