Answer Pages: Show any work that you wish to be graded as well as your answers in the spaces below. Please note, JMP may be used to calculate probabilities. 1) a. Property \#1: \( \qquad \) Property \#2: \( \qquad \) b. The probabality that a randomly selected policatholder files three clains \( P(x=3)=0.04 \) c. The probability that a randomly selected Palicuholdes files more than one claim \( P(x>1)=P(2)+P(3)+(4) \) \( =0.07+0.04+0.01=0.12 \) d. The probabitaty that a pandomly seleoted Pdiacholder fles at most two clains \( 0.50 .95 \quad 0.72+0.016+0.07=0.95 \) c. Mean \( =0.42 \) Standard Deviation \( =0.8623 \) \( \qquad \) \( \qquad \)
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Homework: Chapter #7 7.2.1-T Given a normal distribution with μ = 104 and σ = 20, and given you select a sample of n = 16, complete parts (a) through (d). a. What is the probability that X̄ is less than 90? P(X̄ < 90) = (Type an integer or decimal rounded to four decimal places as needed.) b. What is the probability that X̄ is between 100 and 102.5? c. What is the probability that X̄ is above 112? d. There is a 55% chance that X̄ is above what value?
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A random variable X has a Uniform(a, b) distribution. What characteristics of this random variable are distinctive to this distribution, in the sense that these characteristics would not be guaranteed by any other continuous distribution? The probability density function f(x) integrates to 1 under the sample space of X: ∫[Sx] f(x) dx = 1 The expected value of X can be computed in this way: E(X) = ∫[Sx] xf(x)dx f(x) = 1 / (b - a) The probability density function f(x) is constant for all values of x in the sample space of X. The probability that X takes value in an interval of some length between a and b is the same no matter where that interval is located between a and b. For example, if a = 1 and b = 3, the probability that X takes value in [1, 2] is the same as the probability that X takes value in [2, 3] and also equals the probability that X takes value in [1.5, 2.5]; these are all intervals between a and b of length 1. The probability density function f(x) is such that f(x) ≥ 0 for all x. X takes value in the interval [a, b] where a and b are two real numbers: the probability that X < a and that X > b are zero.
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