solution:
The probability mass function for binomial distribution is,
Where,
X=0,1,2,3,…..; q=1-p
find the probability that (p∧ ≤ 0.06) , substitute the values of sample units (n) , and the probability of nonconformities (p) in the probability mass function of binomial distribution.
Consider x to be the number of non-conformities. It follows a binomial distribution with n being 50 and p being 0.03. That is,
binomial (50,0.02)
Also, the estimate of the true probability is,
p∧ = x/50
The probability mass function for binomial distribution is,
Where,
X=0,1,2,3,…..; q=1-p
The calculation is obtained as
P(p^ ≤ 0.06) = p(x/20 ≤ 0.06)
= 50cx ₓ (0.03)x ₓ (1-0.03)50-x
= (50c0 ₓ (0.03)0 ₓ (1-0.03)50-0 + 50c1(0.03)1 ₓ (1-0.03)50-1 + 50c2 ₓ (0.03)2 ₓ (1-0.03)50-2 +50c3 ₓ (0.03)3 ₓ (1- 0.03)50-3 )
=( ₓ (0.03)0 ₓ (1-0.03)50-0 + ₓ (0.03)1 ₓ (1-0.03)50-1 + ₓ (0.03)2 ₓ (1-0.03)50-2 ₓ (0.03)3 ₓ (1-0.03)50-3 )
The answer is: "11 %" .
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There is 11% of fruit in the cake.
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Explanation:
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275g is what percent of 2.5 kg?
First, convert "275 g" into "kg".
Note the exact conversion: 1000 g = 1 kg .
So 275 g = (275/1000) kg = 0.275 kg .
0.275 kg = (n/100) * 2.5 kg ;
→ (n/100) * 2.5 = 0.275 ;
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Divide each side by "(2.5)"
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→ (n/100) = (0.275) / (2.5) ;
→ (n/100) = 0.11 ;
Multiply each side by "100" ;
n = 11 .
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The answer is: 11 % .
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50% or 1/2 of 4 is 2 50% or 1/2 of 6 is 3 so then just add them to the respective number since its going up by 50% or 2 in by 3 in \[\frac{ 6 }{ 9}\]
