Can you explain/show steps on how to solve these questions?

1. The magnitude of earlhqualtes recorded in a region ofNorth Amer ica can be modeled as having an exponential distribution with mean 2.4. as measured on the Richter scale. Find the probability that aneariquake striking thisregionwill {a} exceed 3.0 on the Ridtter scale. {b} fall between 2.0 and 3.0 on the Richter scale. 2. Suppose that the magnitude of earthquakes striking a region has a gamma dishitmticm with a = 0.8 and I5 = 2.4. {a} 1.I'iihat is the mean magnitude of earthquakes striking the re- gion? {h} 1What is the pmbahility that the magnitude an earthquake strik- ing the region will exceed 3.0 on the Richter scale? {c} What is the probability that an earthquake striking the regions will fall between 2.0 and 3.0 on the Richter scale? {d} Cotnpate these answers to question 1. For examPle. which probabilities are larger? Explain. 3. The number of defective circuit boards coming off a soldering machine follows a Poisson dish'ibution. During a specific eight hour day. one defective circuit board was found. {a} Find the probability that it was produced during the rst hour of operation during the day. {b} Find the pmbability that it was produced during the last hour of operation during the day. {c} Given that no defective circuit boards were produced during the rst four hours of operation. nd the probability that the defective board was manufactured during the fth hour. 4. Wires manufactured for use in a system are specied to have resisr tancesbetween 0.12 and 0.1-1 ft. The actual measured resistanoe of the wires produced by company A have a normal distribution with mean 0.13 D and steeds-rd deviation 0.035 It. {a} 1.I'iihat is the probability that a randomly selected wire from oompmy A's pruducm will meet speu'eatime? {b} \"tourufthesewiresarewedineschsyslemandaarese- lected from company A, whatis the probability that all fourin a randomly selected system will meet the specications