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aksik [14]
3 years ago
12

Each item produced by a certain manufacturer is independently of acceptable quality with probability 0.95. Approximate the proba

bility that at most 10 of the next 150 items produced are unacceptable.
Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
5 0

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: \mu_{\hat p}= p=0.05

The standard deviation of this sampling distribution is: \sigma_{\hat p}=\sqrt{\frac{ p(1-p)}{n}}=\sqrt{\frac{0.05(1-.0.05)}{150} }=0.0178

If 10 of the 150 items produced are unacceptable then the probability of this event is:

\hat p=\frac{10}{150}=0.067

Compute the value of P(\hat p\leq 0.067) as follows:

P(\hat p\leq 0.067)=P(\frac{\hat p-\mu_{p}}{\sigma_{p}} \leq\frac{0.067-0.05}{0.0178})=P(Z\leq 0.96)=0.8315

*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.

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4 0
2 years ago
F(x)=-x^2+8x+15 ...?
rusak2 [61]
Here i how I would do it:<span>f(x)=−<span>x2</span>+8x+15</span>
set f(x) = 0 to find the points at which the graph crosses the x-axis. So<span>−<span>x2</span>+8x+15=0</span>
multiply through by -1<span><span>x2</span>−8x−15=0</span> <span>(x−4<span>)2</span>−31=0</span> <span>x=4±<span>31<span>−−</span>√</span></span>
So these are the points at which the graph crosses the x-axis. To find the point where it crosses the y-axis, set x=0 in your original equation to get 15. Now because of the negative on the x^2, your graph will be an upside down parabola, going through<span>(0,15),(4−<span>31<span>−−</span>√</span>,0)and(4+<span>31<span>−−</span>√</span>,0)</span>
To find the coordinates of the maximum (it is maximum) of the graph, you take a look at the completed square method above. Since we multiplied through by -1, we need to multiply through by it again to get:<span>f(x)=31−(x−4<span>)2</span></span><span>
Now this is maximal when x=4, because x=4 causes -(x-4)^2 to vanish. So the coordinates of the maximum are (4,y). To find the y, simply substitute x=4 into the equation f(x) to give y = 31. So it agrees with the mighty Satellite: (4,31) is the vertex.</span>
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3 years ago
Suppose that you earned a​ bachelor's degree and now​ you're teaching high school. The school district offers teachers the oppor
harkovskaia [24]

Answer:

A ) The Amount which will be saved after five years is $ 5742.4

B ) The compound Interest is $ 1742.4

Step-by-step explanation:

The Principal deposited at the end of each year = $ 4000

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The time period = 5 years

From compounded method :

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or, Amount = $ 4000 × (1+\dfrac{\textrm 7.5}{100})^{\textrm 5}

Or, Amount = $ 4000 × (1.0075)^{5}

or, Amount = $ 4000 × 1.4356

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A ) The Amount which will be saved after five years is $ 5742.4

B ) The compound Interest = Amount - principal

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Write 106,000,000 in scientific notation
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