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
nikdorinn [45]
3 years ago
11

A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly

selects and tests 26 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. What is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 4% rate of defects
Mathematics
1 answer:
Keith_Richards [23]3 years ago
3 0

Answer:

0.7208 = 72.08% probability that this whole shipment will be accepted.

Step-by-step explanation:

For each tablet, there are only two possible outcomes. Either it meets the required specifications, or it does not. The probability of a tablet meeting the required specifications is independent of any other tablet, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

4% rate of defects

This means that p = 0.04

26 tablets

This means that n = 26

What is the probability that this whole shipment will be accepted?

Probability that at most one tablet does not meet the specifications, which is:

P(X \leq 1) = P(X = 0) + P(X = 1)

Thus

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{26,0}.(0.04)^{0}.(0.96)^{26} = 0.3460

P(X = 1) = C_{26,1}.(0.04)^{1}.(0.96)^{25} = 0.3748

Then

P(X \leq 1) = P(X = 0) + P(X = 1) = 0.3460 + 0.3748 = 0.7208

0.7208 = 72.08% probability that this whole shipment will be accepted.

You might be interested in
"Match the inequality with its graph below.
Svetllana [295]
<span>The answers for the given inequalities shown in the figures above are the following: 
1. x+2y is bigger than or equal to 6 corresponds to the first graph.
2. x-2y>4 corresponds to the third graph.
3. y>3+(1/2)x corresponds to the second graph
4. 4y+2x is smaller than or equal to 16 corresponds to the fourth graph</span>
3 0
3 years ago
Use​ l'Hôpital's Rule to find the following limit. ModifyingBelow lim With x right arrow 0StartFraction 3 sine (x )minus 3 x Ove
steposvetlana [31]

Answer:

\lim_{x \to 0} \frac{3sinx-3x}{7x^3}=-\frac{1}{14}

Step-by-step explanation:

The limit is:

\lim_{x \to 0} \frac{3sinx-3x}{7x^3}=\frac{0}{0}

so, you have an indeterminate result. By using the l'Hôpital's rule you have:

\lim_{x \to 0} \frac{a(x)}{b(x)}= \lim_{x \to 0} \frac{a'(x)}{b'(x)}

by replacing, and applying repeatedly you obtain:

\lim_{x \to 0} \frac{3sinx-3x}{7x^3}= \lim_{x \to 0}\frac{3cosx-3}{21x^2}= \lim_{x \to 0}\frac{-3sinx}{42x}= \lim_{x \to 0}\frac{-3cosx}{42}\\\\ \lim_{x \to 0} \frac{3sinx-3x}{7x^3}=\frac{-3cos0}{42}=-\frac{1}{14}

hence, the limit of the function is -1/14

8 0
3 years ago
. Predict the weather that will be at your house when the front has arrived.
FrozenT [24]
As the front approaches, you will have a storm.

I hope this helps!
3 0
2 years ago
SELECT ALL THAT APPLY. In a population of 250 students, 60% are Whites, 20% are Latinos, 15% are Blacks, and 5% others. In a pro
Sophie [7]

In a proportionate stratified sample of 120, there are 72 Whites, 24 Latinos, 18 Blacks and 6  others.

Proportionate Stratified Sample

A proportionate stratified sample is one in which the size of the strata in the sample is proportional to the size of the strata in the population; in other words, the chance of selecting a unit from a stratum depends on the relative size of that stratum in the population.

Calculating the Proportionate Stratified Sample

The given percentage of -

Whites = 60%

Latinos = 20%

Blacks = 5%

Strength of the sample = 120

⇒ Number of Whites = 60% of 120

= 0.6 × 120

=72

Number of Latinos = 20% of 120

= 0.2 × 120

=24

Proportionate Stratified Sample of Blacks and Others

Count of Blacks = 15 % of 120

= 0.15 × 120

= 18

Count of others = 5% of 120

= 0.05 × 120

6

Thus, in a Proportionate Stratified Sample of 120, 72 are Whites, 24 are Latinos, 18 are Blacks, and 6 are others.

Learn more about Proportionate Stratified Sample here:

brainly.com/question/20692763

#SPJ4

6 0
1 year ago
I need help on parallelograms.
Kazeer [188]

y=15

5y-20=2y+25 move terms

5y-2y = 25+20 calculate like terms

3y=45 divide both sides by 3

8 0
3 years ago
Read 2 more answers
Other questions:
  • Find fractions answer
    9·1 answer
  • Plzzzzz help !.!.!.!.!.!.!!..!!.!.!.!.!.!.?
    6·2 answers
  • What is 26.833 rounded to the nearest thousandth?
    15·1 answer
  • What an equation for the translation of y=|x|. 13 unites down
    6·1 answer
  • Please help me. I’ll give brainliest
    11·1 answer
  • If PQ and RS intersect from four right angles which statement is true
    7·1 answer
  • Simplify the complex fraction 7/10÷-2/5
    10·1 answer
  • Solve each of the following equations. Show its solution set on a number line. Check your
    12·1 answer
  • Pease answer quick (only 9.1)
    13·1 answer
  • Are y'all mad or happy about the time change in some places
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!