-18 ponts DevoreSis3.E018 My Noles Some parts of Califonia are particularty arth

Question

-18 ponts DevoreSis3.E018 My Noles Some parts of Califonia are particularty arthquakc-prana. Suppoae that in cne metropolitan arca, 25% of all homcownars are insured against carthquake danage. Four homcownars are to ba selactad at randam. Lat&danate tha number among the four who have (a) Find tha probability distribution of x. [hin: Let S denote a homeowner that has incurance and F onc who doas not. Than ona possible autcome is SFSS, with probability (0.25)0.75a.25)(0.25) and asscciated X valuc 3. There arc 15 other outcomes. (Round your answers to tour dedimal placas. P(x) (b) Draw the corresponding probability histogrom. Probablity 04 03 0 2 0.2 Number with Numberwith earthquake Prohahility Probahiiry 04 03 Number with Numberwith carthquake What is the most likely value forX? (d) What is the probability that at Icast two of the four selected have earthquake incurancc? (Round your answer to four decimal placcs.)

Explanation / Answer

Here for the given binomial distribution

n = 4 and p = 0.25

so here

p(x) = 4Cx (0.25)x (0.75)(4 -x)

now putting values for x = 0 to 4.

p(0) = 0.3164 ; x = 0

= 0.4219 ; x = 1

= 0.2109 ; x = 2

= 0.0469 ; x = 3

= 0.0039 ; x = 4

(b) Here graph C is the correct graph

(c) Most likely value = 1

(d) Pr(at least two out of 4 have earthquake insurance) = Pr(x = 2) + Pr(x = 3) + Pr(x = 4)

= 0.2109 + 0.0469 + 0.0045 = 0.2617

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