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Ivan
3 years ago
7

What are the mean, median, mode, and range of the data set given the altitude of lakes in feet: -11, -28, -17, -25, -28, -39, -6

, and -46?
Mathematics
1 answer:
GrogVix [38]3 years ago
8 0

Answer:

Mean=-21.5

Median=-26.5

Mode=-28

Range= -6 to-46

Step-by-step explanation:

Arranging the numbers given either in ascending or descending order. In this case, I used descending order as follows

-6

-11

-17

-25

-28

-28

-39

-46

Mode is the number that occurs more than others. In this case, only -28 appears twice hence it is the mode

The mean is given by adding all the numbers and dividing by the frequency.

The sum of numbers will be -6+-11+-17+-25+-28+-28+-39+-46=-172

Mean=-172/8=-21.5

The median is the number that appears in the middle after arranging the numbers in descending order as above. In this case, two numbers appear in the middle, that is -25 and -28 hence median -25+-28/2=-26.5

The range of numbers id from -6 to-46 as arranged above

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Answer: 35

Step-by-step explanation:

-3150M-65b+155b

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The mean life of a television set is 119119 months with a standard deviation of 1414 months. If a sample of 7474 televisions is
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Answer:

0.5034 = 50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean

In this problem, we have that:

\mu = 119, \sigma = 14, n = 74, s = \frac{14}{\sqrt{74}} = 1.6275

What is the probability that the sample mean would differ from the true mean by less than 1.11 months?

This is the pvalue of Z when X = 119 + 1.1 = 120.1 subtracted by the pvalue of Z when X = 119 - 1.1 = 117.9. So

X = 120.1

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

By the Central Limit Theorem

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

Z = \frac{120.1 - 119}{1.6275}

Z = 0.68

Z = 0.68 has a pvalue of 0.7517

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

Z = \frac{117.9 - 119}{1.6275}

Z = -0.68

Z = -0.68 has a pvalue of 0.2483

0.7517 - 0.2483 = 0.5034

0.5034 = 50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

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3 years ago
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so the furthest to the right that C extends is the point (5, 2). The line x+y=k passes through this point for 2+5=k\implies k=7. For any value of k, the line x+y=k passes through C either only once, or not at all.

So 7\le k; in set notation,

\{k\mid 7\le k

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