1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Finger [1]
3 years ago
7

Ten percent of the engines manufactured on an assembly line are defective.

Mathematics
1 answer:
antoniya [11.8K]3 years ago
5 0

Answer:

a) the probability that the first non-defective engine will be found on the second trial is 0.09

b) probability that the third non-defective engine will be found on the fifth trial is 0.00486

c) the Mean is 1.1111  and Variance is 0.1235  

d) the Mean is 3.3333and Variance is 0.3704  

Step-by-step explanation:

Firstly;

Let x be the number of trail on which the rth defective occurs

Also let the probability that an occurrence of a defective be p = 0.10

Here, x follows negative binomial distribution with parameters r and p

The probability mass function of X is as follows:

P(X = x) = [ x -1  p^r ( 1 - p)^(x-r)       ; x = r, r + 1, r + 2, ...

                 r - 1 ]

=   [ x -1  (0.10)^r ( 1 - 0.10)^(x-r)

     r - 1 ]

= [ x -1  (0.10)^r ( 0.9)^(x-r)  ..........n 1..... let this be equatio

    r - 1 ]

This represents the probability that the rth success occurs on the xth trail.  

a)

probability that the first non-defective engine will be found on the second trial?

Substitute r = 1 and x = 2 in equation 1  

P(X = 2)  = [ 2 - 1   (0.10)¹ ( 0.90 )²⁻¹

                   1 - 1 ]

= (0.10) × (0.90)

= 0.09

Therefore, the probability that the first non-defective engine will be found on the second trial is 0.09

b)

probability that the third non-defective engine will be found on the fifth trial?

So we substitute r = 3 and x = 5 in equation 1  

P(X = 5) = [ 5 - 1  (0.10)³ ( 0.90)⁵⁻³

                  3 - 1 ]

=    [ 4    (0.10)³ ( 0.9)²

      2 ]

= 0.00486

Therefore, probability that the third non-defective engine will be found on the fifth trial is 0.00486

Now the formula for the mean of the negative binomial distribution is as follows:  

Mean u = r / p    ------- let this be equation 2

The formula for the variance of the negative binomial distribution also is as follows:  

Variance α² = rq / p²   ---------- let this be equation 3

so

c)

the mean and variance of the number of trials on which the first non-defective engine is found.  

First, let the probability that non-defective engine found be p = 0.90

And q = (1 - p) = 1 - 0.90 = 0.10  

Now we substitute r = 1, p = 0.90 and q = 0.10 in equation 2 & 3simultaneously,

the mean and variances are as follows;

Mean = r/p = 1/0.90 = 1.1111

Variance = rq/p² = (1)(0.10) / (0.90)² = 0.1235  

Therefore the Mean is 1.1111  and Variance is 0.1235  

d)

the mean and variance of the number of trials on which the third non-defective engine is found  

Let the probability that non-defective engine found be p = 0.90

And q = (1 - p) = 1 - 0.90 = 0.10

Now we substitute r = 3, p = 0.90 and q = 0.10 in equation (2) and (3) simultaneously,

the mean and variances are;

Mean = r/p = 3/0.90 = 3.3333

Variance = rq/p² = (3)(0.10) / (0.90)² = 0.3704

Therefore the Mean is 3.3333 and Variance is 0.3704    

You might be interested in
3.48 with 8 % tax would equal please help so confused how to do
olga2289 [7]
$3.48 with 8% tax would be 28 cents
6 0
3 years ago
50 PTS PLUS I WILL MARK BRAINLIEST
ch4aika [34]
Subtract 5x to both sides
7 0
3 years ago
Read 2 more answers
Janine inflated a ball to a radius of 18 cm and another ball to a radius of 12 cm.
irina [24]
Thi answer be 753.6 i wish you good marrow
6 0
3 years ago
Population lottery numbers: 56, 42, 19, 8, 24, 13 find the total number of samples of size 4 that can be drawn from this populat
statuscvo [17]

Answer:

The correct answer is there are 15 samples each of size 4 to choose from the population and the population mean is 27.

Step-by-step explanation:

Total number of lottery tickets = 6

Number of samples of size 4 that can be drawn from this population of 6 lottery numbers are = \left[\begin{array}{ccc}6\\4\end{array}\right] = 15.

Now the population mean is given by \frac{1}{n} × ∑ x , where n is the number of lottery tickets and ∑ x  is the sum of the lottery numbers.

Summation of the lottery ticket numbers is 162

Thus the population mean is given by \frac{162}{6} = 27.

8 0
3 years ago
The sum of four consecutive even integer numbers is 84. find the four numbers.
vodomira [7]

84/4=21

 now take the 2 even numbers below 21 and the 2 even numbers above 21

18 +20 + 22 +24 = 84

 the numbers are 18, 20, 22 & 24

3 0
3 years ago
Other questions:
  • Multiply 4x 1/2. And 1/2 x3/4. Also 3/4 x1/3. Please need help with this
    12·2 answers
  • George deposits $3,500 at 3.25% interest compounded monthly. What will his ending balance be after 5 years?
    15·1 answer
  • What is the answer for 6k-9=-15
    15·2 answers
  • Which answer is the equation of the line represented in function notation?
    7·1 answer
  • 5y=15/4x+25<br>1 solution, many solutions, or infinite solutions
    14·1 answer
  • What is y=−7x+8 y=−7x−8 ​
    10·1 answer
  • 13.002 as a fraction
    9·2 answers
  • In one study of 300 coffee drinkers and 150 non coffee drinkers, it was found that only 67 of the coffee drinkers had high blood
    12·1 answer
  • Use the figure shown.
    14·1 answer
  • Which is the slope-intercept equation of the line (-2,2) and (0,-4)?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!