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3 years ago

Determine if events A and B are independent.

Mathematics

1 answer:

trapecia [35]3 years ago

6 0

Answer:

B) Independent

Step-by-step explanation:

Independent events:

Two events, A and B are independent, if:

$P(A \cap B) = P(A) \times P(B)$

In this question:

$P(A \cap B) = \frac{63}{200}$

$P(A) \times P(B) = \frac{9}{20}*\frac{7}{10} = \frac{9*7}{20*10} = \frac{63}{200}$

Since $P(A \cap B) = P(A) \times P(B)$ , these events are independent.

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The LB Company has long manufactured a light bulb with an average life of 5400 hours. Company researchers have recently develope

elena55 [62]

<h2>Answer with explanation:</h2>

Let $\mu$ be the average life of light bulbs.

As per given , we have

Null hypothesis : $H_0 : \mu =5400$

Alternative hypothesis : $H_a : \mu >5400$

Since $H_a$ is right-tailed and population standard deviation is also known, so we perform right-tailed z-test.

Formula for Test statistic : $z=\dfrac{\overlien{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

where, n= sample size

$\overline{x}$ = sample mean

$\mu$ = Population mean

$\sigma$ =population standard deviation

For $n=95,\ \overline{x}=5483\ \&\ \sigma=500$ , we have

$z=\dfrac{5483-5400}{\dfrac{500}{\sqrt{95}}}=1.61796786124\approx1.6180$

Using z-value table , Critical one-tailed test value for 0.06 significance level :

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[We reject the null hypothesis when critical value is less than the test statistic value .]

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