SOLUTION
This is a binomial probability. For i, we will apply the Binomial probability formula
i. Exactly 2 are defective
Using the formula, we have
Note that I made the probability of being defective as the probability of success = p
and probability of none defective as probability of failure = q
Exactly 2 are defective becomes the binomial probability
Hence the answer is 0.1157
(ii) None is defective becomes
hence the answer is 0.4823
(iii) All are defective
(iv) At least one is defective
This is 1 - probability that none is defective
Hence the answer is 0.5177
<span> The product of two perfect squares is a perfect square.
Proof of Existence:
Suppose a = 2^2 , b = 3^2 [ We have to show that the product of a and b is a perfect square.] then
c^2 = (a^2) (b^2)
= (2^2) (3^2)
= (4)9
= 36
and 36 is a perfect square of 6. This is to be shown and this completes the proof</span>
Answer:
6.5
Step-by-step explanation:
7 5/8 + 5 3/8= 13
13/2=6.5
Answer:
The probability that the sample mean would differ from the population mean by more than 2.6 mm is 0.0043.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the distribution of sample mean is given by,
And the standard deviation of the distribution of sample mean is given by,
The information provided is:
<em>μ</em> = 144 mm
<em>σ</em> = 7 mm
<em>n</em> = 50.
Since <em>n</em> = 50 > 30, the Central limit theorem can be applied to approximate the sampling distribution of sample mean.
Compute the probability that the sample mean would differ from the population mean by more than 2.6 mm as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that the sample mean would differ from the population mean by more than 2.6 mm is 0.0043.
-3(-4y+3) +7y
Expand
12y-9+7y
Add like terms
19y-9
