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)1) Please show steps with formulas. hanBs 1. The probability of a dry summer is

ID: 3052406 • Letter: #

Question

)1) Please show steps with formulas. hanBs 1. The probability of a dry summer is equal to 0.3, the probability of a wet summer is equal to 0.2, and the probability of a summer with normal precipitation is equal to 0.5. A climatologist observed the precipitation during three consecutive summers. (a) Enumerate the sample space, and assign probabilities to each simple event (b) What is the probability of observing two dry summers? (c) What is the probability of observing at least two dry summers? (d) What is the probability of not observing a wet summer? 2. Snowfall for a location is found to be normally distributed with mean 96 in and standard deviation 32 in. (a) What is the probability that a given year will have more than 120 inches of (b) What is the probability that the snowfall will be between 90 in. and (c) What level of snowfall will be exceeded only 10% of the time? snow 100 in.?

Explanation / Answer

Let D denote dry summer, W denote wet summer and N denote summer with normal precipitation

a) The events in sample space and theire probabilities are listed below

b) P(2 dry summers) = 3(0.018+0.045)

= 0.189

c) P(at least 2 dry summers) = 0.189 + P(DDD)

= 0.189 + 0.027

= 0.216

d) P(not observing a wet summer = (1-0.2)3

= 0.512

P.S: Please post different questions separately