Mathematics, 15.04.2020 04:09 dchirunga23

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that no more than one in a random sample of four calculators is defective? Multiple Choice 0.2916 0.9477 0.3439 0.6561

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Answer from: jetblackcap

The probability that no more than one in a random sample of four calculators is defective is 0.9477.

Step-by-step explanation:

We can model this as a binomial randome variable, because we have a sum of n Bernoulli variables with probability p of success.

In this case, the sample size is n=4 and the probability of an individual defective calculator is p=0.10.

The probability of having k defective calculators in a sample of n calculators is calculated as:

$P(x=k)=\binom{n}{k}p^k(1-p)^{n-k}$

We have to calculate the probability that no more than one out of four calculators is defective (P(x≤1)). This is the same as adding the probability of having no defective calculator in the sample (P(x=0)) and the probabiltity of having one defective in the sample (P(x=1)):

$P(x\leq 1)=P(x=0)+P(x=1)\\\\\\P(x=0) = \binom{4}{0} p^{0}q^{4}=1*1*0.6561=0.6561\\\\P(x=1) = \binom{4}{1} p^{1}q^{3}=4*0.1*0.729=0.2916\\\\\\P(x\leq 1)=P(x=0)+P(x=1)=0.6561+0.2916=0.9477$

Answer from: Quest

Ithink the answer is a.3: 1i hope this

Answer from: Quest

Answer: f(x) = -2x^3 +3x^2 +11x -6see attachedan infinite number. since the magnitude of the leading coefficient is not specified, it may be any negative number. (we have chosen the smallest magnitude integer that makes all coefficients be integers.)step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

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It is known that 10% of the calculators shipped from a particular factory are defective. What is the...