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anastassius [24]
1 year ago
6

When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 55 bat

teries and determine whether each is within specification. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 3000 batteries, and 2% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
Mathematics
1 answer:
aleksley [76]1 year ago
4 0

The probability of accepting this shipment is 98%.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

Almost all such shipments will be accepted because the probability of having a sample with more than 3 defective batteries is very low.

The shipment will be accepted if at most 3 batteries don't meet specifications.

This can be modeled as a binomial distribution, where the sample size is n=55 and the probability of not meeting the specifications of any battery is p=0.02.

The shipment will be accepted if D ≤ 3.

The probability of this event is:

P( D ≤ 3) = P(D=0) + P(D=1) + P(D=2) + P(D=3)

P(D=X) = n!/(x!(n-x)!) pˣ(1-p)ⁿ⁻ˣ

P(D=0) = 55!/(0!(55-0)!) 0.02⁰(1-0.02)⁵⁵⁻⁰ = 1× 1 × 0.32 = 0.32

P(D=1) = 55!/(1!(55-1)!) 0.02¹(1-0.02)⁵⁴ = 54 × 0.02 × 0.33= 0.35

P(D=2) = 55!/(2!(55-2)!) 0.02²(1-0.02)⁵³ = 55 ×27 × 0.0004 × 0.34= 0.20

P(D=3) = 55!/(3!(55-3)!) 0.02³(1-0.02)⁵² = 25740× 0.0000008 × 0.35= 0.07

Then,

P( D ≤ 3) = P(D=0) + P(D=1) + P(D=2) + P(D=3)

P( D ≤ 3) = 0.32 + 0.35 + 0.20 + 0.07

P( D ≤ 3) = 0.98

Hence, the probability of accepting this shipment is 98%.

To learn more about the probability from the given link

brainly.com/question/24756209

#SPJ1

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Answer:

Division means sharing an item equally. A fraction has two parts - a numerator and a denominator. ... Dividing fractions is almost the same as multiplying them. For the division of fractions, we multiply the first fraction by the reciprocal (inverse) of the second fraction.

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6 0
3 years ago
Ms. McNeil buys 2.4 gallons of gasoline. the total cost is $7.56. Write and solve an equation to find the price p in dollars of
tino4ka555 [31]
If you know the whole price for 2.4 gallons, divide the whole price by 2.4 to get the cost for one, because when you multiply the cost for 1 by 2.4, you get the total. 

7.56/2.4 = 3.15, 

p= 3.15
6 0
3 years ago
What is the solution of the equation?<br><br> 35√(x+2)3+3=27
Arte-miy333 [17]

Use this rule: <em>(x^a)^b = x^ab</em>

3(x + 2)^3/5 + 2 = 27

Subtract 3 from both sides

3(x + 2)^3/5 = 27 - 3

Simplify 27 - 3 to 24

3(x + 2)^3/5 = 24

Divide both sides by 3

(x + 2)^3/5 = 24/3

Simplify 24/3 to 8

(x + 2)^3/5 = 8

Take the cube root of both sides

x + 2 = 3/5√8

Invert and multiply

x + 2 = 8^5/3

Calculate

x + 2 = 2^5

Simplify 2^5 to 32

x + 2 = 32

Subtract 2 from both sides

x = 32 - 2

Simplify 32 - 3 to 30

<u>x = 30</u>

4 0
3 years ago
-144r = -12rk find the value
OLga [1]

k = 12

cancel out the r on both sides

then divide -144 by -12.

you get 12.

5 0
3 years ago
Modern car company has come out with a new car model. Market analysts predict that 4,600 cars will be sold in the first month an
Arte-miy333 [17]

The first five terms of the sequence are; 4,600, 4,550, 4,500, 4,450, 4,400 and the total predicted number of sold cars for the first year is 51,900 cars

<h3>Arithmetic sequence</h3>

  • First month, a = 4,600 cars
  • Common difference, d = -50 cars

First five terms;

a = 4,600

a + d = 4600 + (-50)

= 4600 - 50

= 4,550

a + 2d

= 4600 + 2(-50)

= 4600 - 100

= 4,500

a + 3d

= 4,600 + 3(-50)

= 4,600 - 150

= 4,450

a + 4d

= 4600 + 4(-50)

= 4,600 - 200

= 4,400

cars predicted for the twelfth month.

a + 11d

= 4600 + 11(-50)

= 4600 + 550

= 4,050

Total predicted number of sold cars for the first year:

Sn = n/2{2a + (n - 1)d }

= 12/2{2×4600 + (12-1)-50}

= 6{9200 + 11(-50)}

= 6(9,200 - 550)

= 6(8,650)

= 51,900 cars

Learn more about arithmetic sequence:

brainly.com/question/6561461

#SPJ1

7 0
2 years ago
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