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Rudik [331]
3 years ago
5

Lucy wants to be exempt from her semester exam. In order for that to happen, she has to average an 85 over 3 test grades. Her fi

rst 2 test grades were 81 and 86. What does Lucy need to make on her third test in order to have an exact average of 85 and be exempt from her exam?
Mathematics
1 answer:
anastassius [24]3 years ago
8 0

Answer:

<em>Grades to be scored in 3rd exam = 88</em>

Step-by-step explanation:

Given that average of 3 numbers is 85.

First two numbers are 81 and 86.

To find:

3rd number so that average is 85

Solution:

Let the third number = x

Formula for average is:

Average = \dfrac{Sum\ of\ numbers}{Total\ count\ of\ numbers}

Here, sum of numbers = 81+86+x =167+x

Total count of numbers = 3

85 = \dfrac{167+x}{3}\\\Rightarrow x=255-167\\\Rightarrow \bold{x=88}

<em>Grades to be scored in 3rd exam = 88</em>

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Suppose that, in the past, 40% of all adults favored capital punishment. Do we have reason to believe that the proportion of adu
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Answer:

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Step-by-step explanation:

Suppose that, in the past, 40% of all adults favored capital punishment. Test if the proportion has increased:

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H_1: p > 0.4

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that \mu = 0.4, \sigma = \sqrt{0.4*0.6}

Random sample of 15 adults, 8 favor capital punishment.

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