Mathematics, 27.09.2019 05:30 neariah24

Of all the weld failures in a certain assembly, 85% of them occur in the weld metal itself. asample of 10 weld failures is examined. assume independence of weld failures.(a) what is the probability thatfewer than fourof them are base metal failures? (b) what is the probability thatat least nineof them are base metal failures? (c) find themeanandstandard deviationof the number of base metal failures

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Answer from: AshIeigh

(a) The probability is 0.95

(b) The probability is 0

Step-by-step explanation:

This experiment follows a Binomial distribution in which we have n identical and independent events with two possibles results: success and failure. Then, the probability that x of the n events are success is given by:

$P(x)=nCx*p^{x}*(1-p)^{n-x}$

Where p is the probability of success. Additionally, nCx is calculated as:

$nCx=\frac{n!}{x!(n-x)!}$

So, in this case we have 10 weld failures with a probability 0.85 that it is a weld metal failure and a probability of 0.15 that it is a base metal failure. Then, we are going to call success if the fail is in the base metal so p is equal to 0.15 and n is equal to 10.

(a) The probability that fewer than four of them are base metal failure is the sum of probabilities that 0, 1, 2 and 3 of the 10 weld failures are base metal failures. This is:

P = P(0) + P(1) + P(2) + P(3)

$P=(10C0*0.15^{0} *0.85^{10} )+(10C1*0.15^{1} *0.85^{9} )+(10C2*0.15^{2} *0.85^{8} )+(10C3*0.15^{3} *0.85^{7} )$

P = 0.1969 + 0.3474 + 0.2759 + 0.1298

P = 0.95

(b) The probability that at least nine of them are base metal failures is the sum of probabilities that 9 and 10 of the 10 weld failures are base metal failures. This is:

P = P(9) + P(10)

$P=(10C9*0.15^{9} *0.85^{1} )+(10C10*0.15^{10} *0.85^{0} )$

P ≈ 0

$E(x) =n*p\\S(x) =\sqrt{n*p*(1-p)}$

Then, the values of the mean and standard deviation of the number of base metal failures are:

$E(x) =n*p=10*0.15=1.5 \\S(x) =\sqrt{n*p*(1-p)}=\sqrt{10*0.15*(1-0.15)}=1.1292$

Answer from: Quest

option a is correct.

$\frac{\text{original height}}{\text{original base}}=\frac{\text{reduction height}}{\text{reduction base}}$

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

$\frac{\text{original height}}{\text{original base}}=\frac{\text{reduction height}}{\text{reduction base}}$

Which is the scale factor proportion for the reduction shown? answers are on picture.

Answer from: Quest

play black ops 4 answer a

step-by-step explanation:

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