Write 59/40 as a decimal

The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour

Alexus [3.1K]

Answer:

a) the probability that the defective board was produced during the first hour of operation is $\frac{1}{10}$ or 0.1000

b) the probability that the defective board was produced during the last hour of operation is $\frac{1}{10}$ or 0.1000

c) the required probability is 0.2000

Step-by-step explanation:

Given the data in the question;

During a specific ten-hour period, one defective circuit board was found.

Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.

Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.

f(y) = $\left \{ {{\frac{1}{b-a} }\\\ }} \right _0$ ; ( a ≤ y ≤ b ) $_{elsewhere$

= $\left \{ {{\frac{1}{10-0} }\\\ }} \right _0$ ; ( 0 ≤ y ≤ 10 ) $_{elsewhere$

f(y) = $\left \{ {{\frac{1}{10} }\\\ }} \right _0$ ; ( 0 ≤ y ≤ 10 ) $_{elsewhere$

Now,

a) the probability that it was produced during the first hour of operation during that period;

P( Y < 1 ) = $\int\limits^1_0 {f(y)} \, dy$

we substitute

= $\int\limits^1_0 {\frac{1}{10} } \, dy$

= $\frac{1}{10} [y]^1_0$

= $\frac{1}{10} [ 1 - 0 ]$

= $\frac{1}{10}$ or 0.1000

Therefore, the probability that the defective board was produced during the first hour of operation is $\frac{1}{10}$ or 0.1000

b) The probability that it was produced during the last hour of operation during that period.

P( Y > 9 ) = $\int\limits^{10}_9 {f(y)} \, dy$

we substitute

= $\int\limits^{10}_9 {\frac{1}{10} } \, dy$

= $\frac{1}{10} [y]^{10}_9$

= $\frac{1}{10} [ 10 - 9 ]$

= $\frac{1}{10}$ or 0.1000

Therefore, the probability that the defective board was produced during the last hour of operation is $\frac{1}{10}$ or 0.1000

c)

no defective circuit boards were produced during the first five hours of operation.

probability that the defective board was manufactured during the sixth hour will be;

P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )

= P( 5 < Y < 6 ) / P( Y > 5 )

we substitute

$= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)$

$= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)$

= ( 6-5 ) / ( 10 - 5 )

= 0.2000

Therefore, the required probability is 0.2000

4 0

3 years ago

Which of the following is the minimum value of the equation y = 3x^2 − 4x − 2?

KonstantinChe [14]

Answer:

-3 1/3

Step-by-step explanation:

The quadratic

... y = ax² +bx +c

has its extreme value at

... x = -b/(2a)

Since a = 3 is positive, we know the parabola opens upward and the extreme value is a minimum. (We also know that from the problem statement asking us to find the minimum value.) The value of x at the minimum is -(-4)/(2·3) = 2/3.

To find the minimum value, we need to evaluate the function for x=2/3.

The most straightforward way to do this is to substitue 2/3 for x.

... y = 3(2/3)² -4(2/3) -2 = 3(4/9) -8/3 -2

... y = (4 -8 -6)/3 = -10/3

... y = -3 1/3

_____

<em>Confirmation</em>

You can also use a graphing calculator to show you the minimum.

5 0

3 years ago

Which of the following is closest to the circumference of a circle whose radius is 21 m

Sloan [31]

Here Is your answer!!!!

7 0

3 years ago

Tell Whether the Ordered Pair is (or is NOT) a Solution of the Equation Given<br><br> 3) (-2, -1)

lidiya [134]

you need to include what equation is given

3 0

3 years ago

A ceramics teacher orders 5 blocks of gray clay for every 3 blocks of red clay.

BartSMP [9]

Answer:

25

Step-by-step explanation:

trust me it's right it might be easier if you use paoer

3 0

3 years ago