WHAT IS THE MEAN DEVIATION MAD OF THE DATA SET? { 2, 5, 6, 12, 15}

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let

sergiy2304 [10]

Answer:

(a) P(X=3) = 0.093

(b) P(X≤3) = 0.966

(c) P(X≥4) = 0.034

(d) P(1≤X≤3) = 0.688

(e) The probability that none of the 25 boards is defective is 0.277.

(f) The expected value and standard deviation of X is 1.25 and 1.089 respectively.

Step-by-step explanation:

We are given that when circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%.

Let X = the number of defective boards in a random sample of size, n = 25

So, X ∼ Bin(25,0.05)

The probability distribution for the binomial distribution is given by;

$P(X=r)= \binom{n}{r} \times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,......$

where, n = number of trials (samples) taken = 25

r = number of success

p = probability of success which in our question is percentage

of defectivs, i.e. 5%

(a) P(X = 3) = $\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $2300 \times 0.05^{3}\times 0.95^{22}$

= 0.093

(b) P(X $\leq$ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}+\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $1 \times 1 \times 0.95^{25}+25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}$

= 0.966

(c) P(X $\geq$ 4) = 1 - P(X < 4) = 1 - P(X $\leq$ 3)

= 1 - 0.966

= 0.034

(d) P(1 ≤ X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}$

= 0.688

(e) The probability that none of the 25 boards is defective is given by = P(X = 0)

P(X = 0) = $\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}$

= $1 \times 1\times 0.95^{25}$

= 0.277

(f) The expected value of X is given by;

E(X) = $n \times p$

= $25 \times 0.05$ = 1.25

The standard deviation of X is given by;

S.D.(X) = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{25 \times 0.05 \times (1-0.05)}$

= 1.089

8 0

2 years ago

The first term in a sequence is 5. Each new term in the sequence is obtained by adding 4 to the previous term. Determine an equi

ycow [4]

Answer:

4x+1

Step-by-step explanation:

3 0

2 years ago

(2×4)×7=2×(7×4) what property does this demonstrate

notka56 [123]

Well,

As we can see, the only difference is that the parentheses have moved.

This is an example of the associative property. It is specifically of multiplication, because products are used in this case.

Just as a test, let's see whether they are really equal.

Following PEMDAS, we get:
(2*4)7 = 2(7*4)
(8)7 = 2(28)
56 = 56

They are equivalent.

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3 years ago

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5x-(x+3)=1/3 (9x+18)-5 Please show me step by step

zzz [600]

Step-by-step explanation:

5x-(x+3)=1/3(9x+18)-5

5x-x+3=3x+6-5

1/3 multiplied by 9/1 is three because if you take away the ones and put your problem like this: 9/3, you'll get 3.

1/3 multiplied by 18/1 is six because if you take away the ones and switch to division, it'll look like this: 18/3. 18/3 is 6.

5x-1x+3=3x+6-5

If a variable is alone, you should - in this case - put a one before it, but if the variable is alone you should know that it's automatically a one.

4x+3=3x-1

6-5=1 Simple math problem, probably self explanatory

4x+3=3x-1

Subtract 3x from 4x and you'll get 1x because 4-3 is 1.

1x+3=-1

Then you add 3 to -1 which is 2.

The answer is 1x=2

Or you could've done:

4x+3=3x-1

-4x -4x

3=-1x-1

+-1 +-1

2=1x

It's the same answer, but all I did was subtract the 4x from the 4x and 3x.

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2 years ago

HI HOW ARE YOU MY DUDE!!!

vagabundo [1.1K]

Answer:

I'm fine how are you?

stay safe

7 0

3 years ago

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