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Jobisdone [24]
2 years ago
7

An exam consists of 50 multiple choice questions. Based on how much you studied, for

Mathematics
1 answer:
Ann [662]2 years ago
5 0

Using the Central Limit Theorem, it is found that the sampling distribution of the sample proportion of the 50 questions on which you get the correct is approximately normal, with mean of 0.7 and standard error of 0.0648.

<h3>What does the Central Limit Theorem state?</h3>

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1 - p)}{n}}, as long as np \geq 10 and n(1 - p) \geq 10.

In this problem, we have that p = 0.7, n = 50, hence the mean and the standard deviation are given as follows:

\mu = p = 0.7

s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.7(0.3)}{50}} = 0.0648

More can be learned about the Central Limit Theorem at brainly.com/question/24663213

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8.52 The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches
sweet [91]

Answer:

Heights of 29.5 and below could be a problem.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches.

This means that \mu = 32, \sigma = 1.5

There may be a problem when a child is in the top or bottom 5% of heights. Determine the heights of 2-year-old children that could be a problem.

Heights at the 5th percentile and below. The 5th percentile is X when Z has a p-value of 0.05, so X when Z = -1.645. Thus

Z = \frac{X - \mu}{\sigma}

-1.645 = \frac{X - 32}{1.5}

X - 32 = -1.645*1.5

X = 29.5

Heights of 29.5 and below could be a problem.

4 0
2 years ago
This -1/5(10t-15)and -2t+3 Equivalent???? help please 5 rate??
Serga [27]
Yes, I believe they are equivalent because if you were to solve -1/4(10t-15) it would equal -2t+3
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Answer:

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