Helpp plz i'll mark brainliest (see picture). The second part is, What is the value of y?

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

3 years ago

If you are driving a train and your going over 180 mph, and you pass 20 houses, 10 stores, 3 gas stations, and 1 hospital per ev

zlopas [31]

If I am driving the train , the colour of the eye will be my eye colour.

<h3>What are Logical Questions ?</h3>

The questions that do not need critical reasoning while only need logical thinking to find the answer.

It is given that the "If you are driving a train and your going over 180 mph, and you pass 20 houses, 10 stores, 3 gas stations, and 1 hospital per every ten minutes"

If I am driving the train , the colour of the eye will be my eye colour.

To know more about Logical Questions

brainly.com/question/12087756

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2 years ago

Which expression is equivalent to √-80? 4√5 -4√5 -4i √ 5 4i √ 5

miskamm [114]

Answer:

4i√5

Step-by-step explanation:

$\sqrt{-80}=\sqrt{(-1)(16)(5)}=\sqrt{-1}\cdot\sqrt{16}\cdot\sqrt{5}=4i\sqrt{5}$

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3 years ago

A square is having perimeter 96 cm. Find its area.

nekit [7.7K]

Answer:

348

Step-by-step explanation:

96 multiplied by 4

gives the answer that is 348

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2 years ago

I really need help on this.

Genrish500 [490]

Maybe 50 meters I’m not sure

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2 years ago