The estimate of the population proportion of defectives is 0.05.
Given that,
There are 10 different samples of 50 observations, that is, total of 500 observations.
To find : The estimate of the population proportion of defectives
And total number of defectives from 500 observations is (5+1+1+2+3+3+1+4+2+3) = 25
Thus, the point estimate for the population proportion defectives will be,
=25/500=0.05
or just obtain the individual proportion of each sample and then take their average to obtain the same result.
Thus, the point estimate for the population proportion defectives will be 0.05
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The combined area of these three rooms is 189 ft².
Therefore we have the equation
4x + 3x + 2x = 189
9x = 189 |:9
x = 21 ft²
area of the kitchen = 4x = 4(21) = 84 ft²
area of the playroom = 3x = 3(21) = 63 ft²
area of the dinning room = 2x = 2(21) = 42 ft²
You need to factor the numerator and denominator...
(2x^2+4x-2x-4)/(2x^2-2x-2x+2)
(2x(x+2)-2(x+2))/(2x(x-1)-2(x-1))
((2x-2)(x+2))/((2x-2)(x-1)) so the (2x-2)s cancel out leaving
(x+2)/(x-1)
Since there is replacement, drawings are independent which means that the result of one of them does not affect the others.
Probability of drawing an apple is 4/10 (4 apple out of 10 fruits)
Probability of drawing an apricot is 2/10
Probability on one happening consecutively to the other (thanks to independence) is 4/10*2/10=8/100
Which can be simplified to 2/25
