<span>When you are sampling from a small finite lot, the hypergeometric distribution applies. The binomial is a poor approximation in this case.
The general equation for the hypergeometric where aCx means the number of combinations of a items selected x at-a-time.:
P(x) =[(aCx)(N-aCn-x)]/NCn
Where
N is the lot size = 20
a is the number of defectives in the lot = 3.
x is the number of defectives in the sample.
n is the sample size = 2.
A. The probability that the first item is defective is
P(x=1) = [(3C1)(17C1)]/(20C2)
= (3)(17)/190 = 0.268
The probability that the second item is defective is
P(x = 1) = [(2C1)(17C1)]/(19C2) = (2)(17)/171 = 0.199.
So the total probability is (0.268)(0.199) = 0.0532
B. The probability that the first item is good is:
P(x = 0) = (3C0)(16C2)]/20C2 = (1)(120)/190 = 0.632
The probability that the second item is defective is
P(x = 0) =[(3C0)(16C2)]/19C2
= (1)(120)/171 = 0.670.
The total probability is 0.632(0.670) = 0.4234</span>
When the variance of a sample of 144 observation is 576 then, the standard deviation of the sample equals 24
The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean. Variance tells you the degree of spread in your data set
Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Given,
The number of samples = 144
The variance = 576
The standard deviation is the square root of variance
The standard deviation = 
=24
Hence, when the variance of a sample of 144 observation is 576 then, the standard deviation of the sample equals 24
Learn more about Standard deviation here
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Move the variable to one side by finding common denominator
1/4 - 7/10p = 1/20p
5/20 - 14/20p = 1/20p
+ 14/20p +14/20p
5/20 = 15/20p
Simplify
1/4 = 3/4 p
multiply both sides by 4, then divide both sides by 3
1 = 3p
1/3 = p
Answer:
Step-by-step explanation:
y - 8 = -2/3(x + 3)
the solution is the 4th option
Pat is 38 and James is 18
38+2=40
18+2=20
