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Pr[Z < 1.02] = Pr[Z < 0] + Pr[0 < Z < 1.02] = 0.50+0.3461=0.8461(d)Pr[0.60 < Z < 1.4] = Pr[0 < Z < 1.4] – Pr[0 < Z < 0.60] = 0.4192−0.2257=0.1935(e)Pr[-2 < Z < 2] = Pr[0 < Z < 2] x 2 = 0.4772x2=0.9544(f)Pr[Z < 0.45] = Pr[Z < 0] + Pr[0 < Z < 0.45] = 0.50+0.1736=0.6736(g)Pr[-0.2 < Z < 0.37] = [-0.2 < Z < 0] + Pr[0 < Z < 0.37] = Pr[0 < Z < 0.2] + Pr[0 < Z < 0.37] =0.0793+0.1443=0.2236(h)Question 4 [Statement]: The highest recorded temperature during the month of July for a given year in Death Valley, in California, has an approximately normal distribution with a mean of 123.8℉(NO WAY!) and standard deviation of 3.1℉(Weather Source 2009).Questions: (A) What is the probability for a given year that the temperature never exceeds 120℉in a3
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given July in Death Valley? (B) What is the probability that the temperature in Death Valley goes above 128℉duringJuly in a randomly chosen year?Answers: (A) The following computation has been carried out in order to find the probability that the temperature never exceeds 120℉in a given July in Death Valley: Pr[X ≤120]=Pr [X−μσ≤(120−123.8)(3.1)]= Pr [Z ≤−1.2258]= 0.109349; therefore, the probability that the temperature in Death Valley never exceeds 120℉is0.109349. (B) The following computation has been carried out in order to find the probability that the temperature ever exceeds 128℉during July in a randomly chosen year in Death Valley:Pr[X>128]=1−Pr[X ≤128]=1−Pr[X−μσ≤(128−123.8)(3.1)]=1−Pr [1≤1.35]Pr[X>128]=1−Pr[Z≤1.35]=1−0.911492=0.088508; therefore, the [Please Note: please continue to next page to find the rest of question #15 and end of assignment]probability that the temperature in Death Valley never exceeds 128℉during a randomly chosen year is 0.0885. [END OF ASSIGNMENT 10] 4
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