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Answer:
The probability that at most 10 of the next 150 items produced are unacceptable is 0.8315.
Step-by-step explanation:
Let <em>X</em> = number of items with unacceptable quality.
The probability of an item being unacceptable is, P (X) = <em>p</em> = 0.05.
The sample of items selected is of size, <em>n</em> = 150.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 150 and <em>p</em> = 0.05.
According to the Central limit theorem, if a sample of large size (<em>n</em> > 30) is selected from an unknown population then the sampling distribution of sample mean can be approximated by the Normal distribution.
The mean of this sampling distribution is:
The standard deviation of this sampling distribution is:
If 10 of the 150 items produced are unacceptable then the probability of this event is:
Compute the value of as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that at most 10 of the next 150 items produced are unacceptable is 0.8315.
The expression can be divided by one and itself only. Then the expression is a prime expression. The correct option is C.
<h3>What is a factorization?</h3>It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The expression is
The expression can be written as
The expression can not be the real factor.
Since the expression can be divided by one and itself only.
Then the expression is a prime expression.
Thus, the correct option is C.
More about the factorization link is given below.