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2 years ago

The odds against a particular event happening are 9 : 7. What is the probability that the event will happen?

Mathematics

1 answer:

Vsevolod [243]2 years ago

7 0

Answer:

7/16

Step-by-step explanation:

Odds against = number of failures / number of successes

So number of failures = 9 and the number of successes = 7.

Probability = number of successes / number of total events

P = 7 / (7 + 9)

P = 7/16

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Two people can swing on a trapeze at the same time as long as

pychu [463]

Answer:

Yes!

Step-by-step explanation:

Joe’s weight with Jake’s weight is 490, which is less than 500, so yes!

4 0

2 years ago

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In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A

Marina86 [1]

Answer:

(a) 0.94

(b) 0.20

Step-by-step explanation:

From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let $p_1$ be the probability that a bearing meets the specification.

So, $p_1=0.9$

Sample size, $n_1=500$ , is large.

Let X represent the number of acceptable bearing.

Convert this to a normal distribution,

Mean: $\mu_1=n_1p_1=500\times0.9=450$

Variance: $\sigma_1^2=n_1p_1(1-p_1)=500\times0.9\times0.1=45$

$\Rightarrow \sigma_1 =\sqrt{45}=6.71$

(a) A shipment is acceptable if at least 440 of the 500 bearings meet the specification.

So, $X\geq 440.$

Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.

$z=\frac{x-\mu}{\sigma}=\frac{339.5-450}{6.71}=-1.56$ .

So, the probability that a given shipment is acceptable is

$P(z\geq-1.56)=\int_{-1.56}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}}=0.94062$

Hence, the probability that a given shipment is acceptable is 0.94.

(b) We have the probability of acceptability of one shipment 0.94, which is same for each shipment, so here the number of shipments is a Binomial population.

Denote the probability od acceptance of a shipment by $p_2$ .

$p_2=0.94$

The total number of shipment, i.e sample size, $n_2= 300$

Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, $\mu_2$ , and variance, $\sigma_2^2$ .

Mean: $\mu_2=n_2p_2=300\times0.94=282$

Variance: $\sigma_2^2=n_2p_2(1-p_2)=300\times0.94(1-0.94)=16.92$

$\Rightarrow \sigma_2=\sqrt(16.92}=4.11$ .

In this case, X>285, so, by using the continuity correction, take x=285.5 to compute z score for the normal distribution.

$z=\frac{x-\mu}{\sigma}=\frac{285.5-282}{4.11}=0.85$ .

So, the probability that a given shipment is acceptable is

$P(z\geq0.85)=\int_{0.85}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}=0.1977$

Hence, the probability that a given shipment is acceptable is 0.20.

(c) For the acceptance of 99% shipment of in the total shipment of 300 (sample size).

The area right to the z-score=0.99

and the area left to the z-score is 1-0.99=0.001.

For this value, the value of z-score is -3.09 (from the z-score table)

Let, $\alpha$ be the required probability of acceptance of one shipment.

So,

$-3.09=\frac{285.5-300\alpha}{\sqrt{300 \alpha(1-\alpha)}}$

On solving

$\alpha= 0.977896$

Again, the probability of acceptance of one shipment, $\alpha$ , depends on the probability of meeting the thickness specification of one bearing.

For this case,

The area right to the z-score=0.97790

and the area left to the z-score is 1-0.97790=0.0221.

The value of z-score is -2.01 (from the z-score table)

Let $p$ be the probability that one bearing meets the specification. So

$-2.01=\frac{439.5-500 p}{\sqrt{500 p(1-p)}}$

On solving

$p=0.9053$

Hence, 90.53% of the bearings meet a thickness specification so that 99% of the shipments are acceptable.

8 0

3 years ago

Lol plsss help me :((

patriot [66]

Answer:

The choice two;

$- \sqrt{3}$

Step-by-step explanation:

$\sqrt{27} - 4 \sqrt{3} \\ 3 \sqrt{3} - 4 \sqrt{3} = - 1 \sqrt{3} = - \sqrt{3}$

6 0

2 years ago

Christine has a rectangular poster. The poster is 1.5 meters long and 1.2 meters wide. What is the area of the poster in square

Setler79 [48]

Answer: 180cm^2

Explanation: First, multiply 1.5 by 1.2 to get the area of the rectangle in METERS, which is 1.8. Since the question is asking for the area in CENTIMETERS, multiply 1.8 by 100 (because 1 meter=100 centimeters) to get 180cm^2.

Hope that helped :)

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2 years ago

Can sum1 answer asap and pls give explanation :)

Tju [1.3M]

Answer:

whats the question

Step-by-step explanation:

6 0

2 years ago

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