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STAT 10-10-16

Probability (Test 1)

Normal distribution Finding percentiles on the computer
Suppose X~N(100, 49), find P(x < k) = .1 Minitab graph probability distribution plot
Suppose X~N(100, 49), find P(x > k) = .4 Minitab graph probability distribution plot
Suppose X~N(100, 49), find P(a < x < b) = .95 Minitab graph probability distribution plot
Bernoulli’s rule On a random experiment, there are two possible outcomes (e.g. True or False), usually expressed as success or failure with probability of success p
X~N(100,49), P(x<k) = .1 =NORMINV(0.1,100,7)
X~N(100,49), P(x>k) = .4 =NORMINV(0.6,100,7)
X~N(100,49), P(a<x<b) = .95 → a =NORMINV(0.025,100,7)
X~N(100,49), P(a<x<b) = .95 → b =NORMINV(0.975,100,7)
If x~Bern(p), then the possible values are zero and one
P(x = 1) = p
P(x = 0) = 1 - p = q
μ = p
σ² = p(1 - p)
Binomial distribution>>binomial experiment is to repeat independent and identical Bernoulli experiments a predetermined number of times, n
Binomial experiment example flip a coin 10 times
Binomial random variable number of successes on these n trials
Binomial random variable example x is the number of heads on 10 flips
In general, if x~b(n, p), then the possible values for x are 0, 1, 2, …, n
X~b(15, .7), P(x = 3) =BINOM.DIST(3,15,0.7,0)
X~b(15, .7), P(x = 15) =BINOM.DIST(15,15,0.7,0)
X~b(15, .7), P(x <= 14) =BINOM.DIST(14,15,0.7,1)
X~b(15, .7), P(x < 12) =BINOM.DIST(11,15,0.7,1)
X~b(15, .7), P(x < 15) =BINOM.DIST(14,15,0.7,1)
0 cumulative in excel equal to
1 cumulative in excel less than or equal to
Less than cumulative in excel 1 - probability number
Created by: Spencer Gowey Spencer Gowey