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GuDViN [60]
2 years ago
5

Solve the following proportion for y.y/5 = 7/8Round your answer to the nearest tenth.

Mathematics
1 answer:
Vinvika [58]2 years ago
3 0

The given proportion is expressed as

y/5 = 7/8

If we crossmultiply, it becomes

y * 8 = 7 * 5

8y = 35

y = 35/8

y = 4.375

Rounding to the nearest tenth,

y = 4.4

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If the lot has 4 defective covers out of 25 total covers, the probability of accepting the lot is P=0.98.

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We have a population of N=25 skylight covers, were K=4 are defective.

We sample n=5 covers, and we will accept the lot if k=2 or fewer are defective.

We will use the hypergeometric distribution to model this probabilities.

First, to be accepted, the sample can have 2, 1 or 0 defective covers, so the probability of being accepted is:

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The probability that there are k defective covers in the sample is:

P(k)=\dfrac{\dbinom{k}{k}\dbinom{N-k}{n-k}}{\dbinom{N}{n}}

Then, we can calculate the individual probabilities as:

P(k=0)=\dfrac{\dbinom{4}{0}\cdot \dbinom{25-4}{5-0}}{\dbinom{25}{5}}=\dfrac{\dbinom{4}{0}\cdot \dbinom{21}{5}}{\dbinom{25}{5}}\\\\\\P(k=0)=\dfrac{1\cdot 20349}{53130}=0.38

P(k=1)=\dfrac{\dbinom{4}{1}\cdot \dbinom{25-4}{5-1}}{\dbinom{25}{5}}=\dfrac{\dbinom{4}{1}\cdot \dbinom{21}{4}}{\dbinom{25}{5}}\\\\\\P(k=1)=\dfrac{4\cdot 5985}{53130}=0.45

P(k=2)=\dfrac{\dbinom{4}{2}\cdot \dbinom{25-4}{5-2}}{\dbinom{25}{5}}=\dfrac{\dbinom{4}{2}\cdot \dbinom{21}{3}}{\dbinom{25}{5}}\\\\\\P(k=2)=\dfrac{6\cdot 1330}{53130}=0.15

If we add this probabilities, we have:

P(accepted)=P(k\leq2)=P(k=0)+P(k=1)+P(k=2)\\\\P(accepted)=0.38+0.45+0.15=0.98

If the lot has 4 defective covers out of 25 total covers, the probability of accepting the lot is P=0.98.

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3 years ago
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