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2 years ago

2020-21

Mathematics

1 answer:

Dvinal [7]2 years ago

5 0

Answer: Brain paid $ 45.5 for the jacket.

Step-by-step explanation:

Given: Original price of jacket = $ 65

Discount -= 30%

Price after discount = Original price - 30% of Original price

= 65 - 30% of 65

= 65 - (0.3) x 65 [30% = 0.3]

= (65) (1-0.3 ) [Taking 65 common]

= (65)(0.7)

= $ 45.5

Hence, Brain paid $ 45.5 for the jacket.

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Hi there.

I'm just going to put the answer for now. I might come back and edit my answer if I figure out how to solve this the long way.

All I did was figure out what exponent you raise 10 to.

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Edit:

I did it on paper - here it is broken down.

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2 years ago

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A simple random sample of 100 8th graders at a large suburban middle school indicated that 87% of them are involved with some ty

UkoKoshka [18]

Answer:

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And the margin of error is given by:

$ME = 1.96 *\frac{0.87*(1-0.87)}{100} = 0.0659$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And the margin of error is given by:

$ME = 1.96 *\frac{0.87*(1-0.87)}{100} = 0.0659$

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