Question

A tidal wave or tsunami is usually the result of an earthquake in the Pacific Rim, often 1000 or more miles from Hawaii. Tsunamis are rare but dangerous. Many tsunamis are small and do little damage. However, a tsunami nine meters or higher is very dangerous. Civil Defense authorities sound an alarm telling people near the beach to go to higher ground. About 30% of all recorded tsunamis have been nine meters or higher.† You are writing a report about eight recent earthquakes in the Pacific Rim and you want to include a brief statistical profile of some possible events regarding tsunamis in Hawaii. Let r be the number of tsunamis nine meters or higher resulting from eight randomly chosen earthquakes in the Pacific Rim. (a) Make a histogram of the probability distribution of r. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (b) What is the probability none of the tsunamis are nine meters or higher? (Round your answer to three decimal places.) (c) What is the probability at least one is nine meters or higher? (Round your answer to three decimal places.) (d) What is the expected number of tsunamis nine meters or higher? (Round your answer to two decimal places.) tsunamis (e) What is the standard deviation of the r-probability distribution? (Round your answer to three decimal places.) tsunamis

Answer 1

Solution : 30% of all recorded tsunamis have been 9 mtrs or higher

P(r = a) = 8Ca*0.30a*(1-0.30)8-a

r	P(r)
0	0.058
1	0.198
2	0.296
3	0.254
4	0.136
5	0.047
6	0.010
7	0.001
8	0.000

a)

From the above data, the histogram will be :

b) The probability none of the tsunamis are nine meters or higher is

P(r = 0) = (8r0)(0.30)0(1-0.30)8-0

= 1*1*0.0576

= 0.058

c) The probability that atleast one of the tsunamis are nine meters or higher is

P (r >=1 ) = 1 - P(r = 0)

= 1 - 0.058

= 0.942

d) The expected number of tsunamis are nine meters or higher = np

= 8*0.30

= 2.40

e) Standard deviation of the r- probability distribution = √npq , where q = (1-p) = (1-0.30)

= √8*0.30*(1-0.30)

= √1.68

= 1.296