Homework Assignment #10.docx

# 02 prz 0 pr0 z 102 050 03461 08461 d pr060 z 14 pr0 z

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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 = 0.4772 x 2 = 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 a 3

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given July in Death Valley? ( B ) What is the probability that the temperature in Death Valley goes above 128 during July 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 μ σ ( 120 123.8 ) ( 3.1 ) ] = Pr [ Z ≤ 1.2258 ] = 0.109349 ; therefore, the probability that the temperature in Death Valley never exceeds 120 is 0.109349 . ( 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 μ σ ( 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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