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
Svetradugi [14.3K]
3 years ago
7

Ninety-one percent of products come off the line within product specifications. Your quality control department selects 15 produ

cts randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired?Fewer than 10Fewer than 12Fewer than 11Fewer than 9
Mathematics
1 answer:
Allisa [31]3 years ago
8 0

Answer:

Probability of stopping the machine when X < 9 is 0.0002

Probability of stopping the machine when X < 10 is 0.0013

Probability of stopping the machine when X < 11 is 0.0082

Probability of stopping the machine when X < 12 is 0.0399

Step-by-step explanation:

There is a random binomial variable X that represents the number of units come off the line within product specifications in a review of n Bernoulli-type trials with probability of success 0.91. Therefore, the model is {15 \choose x} (0.91) ^ {x} (0.09) ^ {(15-x)}. So:

P (X < 9) = 1 - P (X \geq 9) = 1 - [{15 \choose 9} (0.91)^{9}(0.09)^{6}+...+{ 15 \choose 15}(0.91)^{15}(0.09)^{0}] = 0.0002

P (X < 10) = 1 - P (X \geq 10) = 1 - [{15 \choose 10}(0.91)^{10}(0.09)^{5}+...+{15 \choose 15} (0.91)^{15}(0.09)^{0}] = 0.0013

P (X < 11) = 1 - P (X \geq 11) = 1 - [{15 \choose 11}(0.91)^{11}(0.09)^{4}+...+{15 \choose 15} (0.91)^{15}(0.09)^{0}] = 0.0082

P (X < 12) = 1- P (X \geq 12) = 1 - [{15 \choose 12}(0.91)^{12}(0.09)^{3}+...+{15 \choose 15} (0.91)^{15}(0.09)^{0}] = 0.0399

Probability of stopping the machine when X < 9 is 0.0002

Probability of stopping the machine when X < 10 is 0.0013

Probability of stopping the machine when X < 11 is 0.0082

Probability of stopping the machine when X < 12 is 0.0399

You might be interested in
The quarterly returns for a group of 6161 mutual funds are well modeled by a Normal model with a mean of 6.16.1​% and a standard
Shtirlitz [24]

Answer:

a) The cut off value of the highest 50% is 6.16%.

b) The cut off value of the highest 16% is 8.8%.

c) The cut off value of the lowest 2.5% is 0.7%.

d) The cut off values of the middle 68% is 3.4% for the lower bound and 8.8% for the higher bound.

Step-by-step explanation:

The 68–95–99.7 rule is an empirical rule to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations respectively.

a) Cut off value of the highest 50%

It corresponds to the half that has the higher returns, which are the ones that are above the mean (0 standard deviation). The cut off value in this case is the mean x=6.16%.

b) Cut off value of the highest 16%

In this case, we use the 68 rule-value, which means that 68% of the values lies within a band around the mean with a width of two standard deviations.

The percentage that lies out of this band is 100%-68%=32%, of which 16% lies above the band (the highest 16%) and 16% lies below the band.

We can estimate, according to this rule, that the highest 16% are above the cutoff value X of μ+1σ:

X=\mu+\sigma=6.1%+2.7%=8.8%

The cut off value of the highest 16% is 8.8%.

c) Cut off of the lowest 2.5%

In this case, we use the 95 rule.

The lowest 2.5% lies below two standards deviation less of the mean

X=\mu-2*\sigma=6.1%-2*2.7%=0.7%

The cut off value of the lowest 2.5% is 0.7%.

d) Cut off of the middle 68%

In this case we calculate the band within one standard deviation.

X_{low}=\mu-\sigma=6.1%-2.7%=3.4%\\\\X_{high}=\mu+\sigma=6.1%+2.7%=8.8%

The cut off values of the middle 68% is 3.4% for the lower bound and 8.8% for the higher bound.

6 0
3 years ago
Is this right I'm practicing multiplying decimals by 10, 100, or 1,000
Leokris [45]
All are correct except the bottom, it would just be 4.23 since there are no zeroes, any number times 1 is itself
8 0
3 years ago
A gift box has the shape of a cube with an edge length of 4.5 in.
DIA [1.3K]

Answer:

4.5 times 4.5 times 4.5 = 91.125

Step-by-step explanation

To find the volume you do v= length times width times height.

6 0
2 years ago
Read 2 more answers
PLEASE WILL MARK BRAINLIEST Find angle MPQ
kiruha [24]

Answer:

Obtuse Angle.

-16.66666667

Step-by-step explanation:

4 0
3 years ago
- Keisha has four letter cards that spell out the word MATH. Keisha picks four cards, one at a
zubka84 [21]

Answer:

1/24

Step-by-step explanation:

1/4 x 1/3 x 1/2 x 1/1

1/24

5 0
2 years ago
Other questions:
  • Pleas help me if you can’t see the picture it’s h over 10 as a fraction then it says=100 what is h?
    8·2 answers
  • 55% of what number is 1100? Which of the following proportions could be used to solve this problem?
    8·1 answer
  • Two increased by six times a number 
    6·2 answers
  • You deposit $100 in an account earning 4% interest compounded annually. How much will you have in the account in 10 years? Round
    9·1 answer
  • What is the slope of the line described by the equation below?
    8·1 answer
  • Please help me. I’ll mark brainliest!!!
    7·1 answer
  • Algebra. Find the values of the variable
    14·1 answer
  • Marissa and Jarod plan to purchase DVD players with a regular price of $199.99. The DVD players are on sale for 25% off. Marissa
    13·1 answer
  • Plz help will be marked BRAINLIEST!!<br> Thanks man!
    9·2 answers
  • 7. Find the difference between the compound interest and simple interest on 1,20,000 for 3/2 years at the rate of 4% per annum.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!