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ankoles [38]
3 years ago
14

Researchers are concerned about the binge drinking behaviors at a local university among members of Greek life organizations. As

sume the college reported that binge drinking was observed in 31% of students attending the university. The research team conducts a sample of 213 students involved in a Greek life organization on campus and finds that 94 have reported binge drinking behaviors at least once that year. Can researchers carry out their analysis assuming an approximation to the normal distribution is acceptable?
Calculate the probability of observing the results witnessed in the sample.
Determine the mean and standard deviation for this distribution under the assumption made under the normal approximation. If the Normal approximation is not applicable, state "Not Applicable".
Mathematics
1 answer:
Evgen [1.6K]3 years ago
6 0

Answer:

The normal approximation is applicable.

The probability of observing the results witnessed in the sample is P=0.00002.

Step-by-step explanation:

They can carry out their analysis assuming an approximation to the normal distribution because the sample size (n=213) is big enough. It would be very cumbersome to use binomial distribution with that sample size.

To calculate the probability of observing the results witnessed in the sample, we have to define the parameters of the sampling distribution, approximating this to a normal distribution:

\mu=\pi=0.31\\\\\sigma=\sqrt{\frac{\pi(1-\pi)}{N} } =\sqrt{\frac{0.31(1-0.31)}{213}}=0.032

The proportion of the sample is:

p=94/213=0.44

We can calculate the z-value:

z=\frac{X-\mu}{\sigma} =\frac{0.44-0.31}{0.032}=\frac{0.13}{0.032}=4.062

The probability value for z>4.062 is equal to the probability of having a sample mean of 94 or more:

P(X>94)=P(z>4.062)=0.00002

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Answer:

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Step-by-step explanation:

An equation always contains an equal sign, so in this case, if it doesn't contain an equal sign, it's an expression.

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8 0
3 years ago
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Answer:

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3 years ago
The midpoint, M , of segment AB has coordinates (2,−1) . If endpoint A of the segment has coordinates (−3,5) , what are the coor
lbvjy [14]

the coordinates of endpoint B are (7,7)

Answer:

Solution given:

M(x,y)=(2,-1)

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now

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$ubstituting value

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Which phrase best describes the translation from the graph y = (x – 5)2 + 7 to the graph of y = (x + 1)2 – 2?
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The parent. function shifted up by 6 units to produce x + 1 and to the left by 9 units

<h3>What is translation?</h3>

This is a way of changing the position of an object on an xy-plane.

Given the parent function expressed as  y = (x – 5)^2 + 7

From the resulting image after translation, we can see that the parent. function shifted up by 6 units to produce x + 1 and to the left by 9 units

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