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1 year ago

(Scientific Notation in the Real World MC)

Mathematics

1 answer:

Brrunno [24]1 year ago

5 0

The average number of viewers over the two week is D. 4.85 x 10^5.

<h3>How to calculate the value?</h3>

It should be noted that the scientific notation simply has to do with writing of numbers that are either too large or too small. This will be illustrated thus:

In this case, the TV show had 5.6 x 10^5 viewers in the first week and 4.1 x 10^5 viewers in the second week.

Therefore, the average number of viewers over the two weeks will be:

= (5.6 × 10^5) + (4.1 × 10^5) / 2

= 4.85 × 10^5

Note that we had to divide by 2 since it's average.

Learn more about notation on:

brainly.com/question/5756316

#SPJ1

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djverab [1.8K]

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$(242-220) -1.988 \sqrt{\frac{20^2}{47} +\frac{31^2}{42}}= 10.862$

$(242-220) +1.988 \sqrt{\frac{20^2}{47} +\frac{31^2}{42}}= 33.138$

And the 95% confidence interval for the difference in the means is given by: $10.862 \leq \mu_A -\mu_B \leq 33.138$

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.

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$\bar X_A = 242$ sample mean for inhibitor A

$s_A = 20$ sample standard deviation for inhibitor A

$n_A = 47$ sample size for A

$\bar X_B = 220$ sample mean for inhibitor B

$s_B = 31$ sample standard deviation for inhibitor B

$n_B = 42$ sample size for A

Solution to the problem

For this case the confidence interval for the difference of means is given by:

$(\bar X_A -\bar X_B) \pm t_{\alpha/2} \sqrt{\frac{s^2_A}{n_A} +\frac{s^2_B}{n_B}}$

The degrees of freedom are given by:

$df = n_A +n_B -2 = 47+42-2= 87$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,87)".And we see that $t_{\alpha/2}=1.988$

And replacing we got:

$(242-220) -1.988 \sqrt{\frac{20^2}{47} +\frac{31^2}{42}}= 10.862$

$(242-220) +1.988 \sqrt{\frac{20^2}{47} +\frac{31^2}{42}}= 33.138$

And the 95% confidence interval for the difference in the means is given by: $10.862 \leq \mu_A -\mu_B \leq 33.138$

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