Question

ofalltheweldfailuresinacertainassembly,85%of them occur in the weld metal itself, and the remaining 15% occur in the base metal. a sample of 20 weld failures is examined. a. whatistheprobabilitythatexactlyfiveofthemare base metal failures? b. whatistheprobabilitythatfewerthanfourofthem are base metal failures? c. whatistheprobabilitythatnoneofthemarebase metal failures?

Answer 1

The probability that exactly five if then are base metal failures is 0.1028

Given that,

The weld metal itself accounts for 85% of all weld failures in a given assembly, with the base metal accounting for the remaining 15%. Weld failures from 20 samples are analyzed.

X : number of base metal failures.

X ~ bin (n,p)

where, n = 20, p =0.15, q = 0.85

the pmf be:-

P(X=x)=$\binom{20}{x}*0.15^x*0.85^{20-x}$

a)The probability that exactly five if then are base metal failures be:-

P(X=5)=$\binom{20}{5}*0.15^5*0.85^{20-5}\approx \mathbf{0.1028}$

b)The probability that fewer than three of them are base metal failures be:-

=P(X<3)

=P(X=0)+P(X=1)+P(X=2)

$\approx \mathbf{0.4049}$

c)The mean number of base metal failures be:-

=np=(20*0.15)=$\mathbf{3}$

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