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 )
Answer:
x = 10
Step-by-step explanation:
l n 20 + l n 5 = 2 l n x
ln (20×5) = ln x²
ln(100) = lnx²
100 = x²
x = +/- 10
Since logs of negative numebrs don't exist, we reject -10
Question:
The square of a number decreased by 3 times the number is 28 find all possible values for the number
Answer:
The possible values of number are 7 and -4
Solution:
Given that the square of a number decreased by 3 times the number is 28
To find: all possible values of number
Let "a" be the unknown number
From given information,
square of a number decreased by 3 times the number = 28
Let us solve the above quadratic equation
Using the above formula,
Thus the possible values of number are 7 and -4
