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trapecia [35]
2 years ago
5

the length of a rectangular swimming pool is triple its width the pool covers an area of 192 m squared

Mathematics
1 answer:
SCORPION-xisa [38]2 years ago
3 0
Hope this helps you!

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Jumbo eggs in Australia, on average, are supposed to weigh 68g. Margot is in charge of a quality control test that involves weig
Andrej [43]

Answer:

0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g

Step-by-step explanation:

To solve this question, we use the normal probability distribution and the central limit theorem.

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 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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean weight of 67g and a sample standard deviation of 1g.

This means that \mu = 67, \sigma = 1

Sample of 4

This means that n = 4, s = \frac{1}{\sqrt{4}} = 0.5

What is the probability that the mean weight of 4 eggs in a package is less than 68.5g?

This is the pvalue of Z when X = 68.5. So

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

By the Central Limit Theorem

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

Z = \frac{68.5 - 67}{0.5}

Z = 3

Z = 3 has a pvalue of 0.9987

0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g

6 0
3 years ago
Read 2 more answers
The model represents the equation x - 1 < -4. What is the solution for the inequality?
Step2247 [10]

Answer:

any number equal to or less than -4

Step-by-step explanation:

x - 1 < -4

< represents that -4 is a larger number than x - 1. we know that -4 is a negative number, so anything below -4 would be less. x = -4 would be a good solution, but the reality is that any number equal to or less than -4 is the correct answer. I hope this helps!

7 0
2 years ago
Standard sheet of paper in the United States is 11 inches long and 8.5 inches wide. Each inch is 2.54 cm. How long and wide is a
Virty [35]
27.94 cm long, 21.59 long :]
3 0
3 years ago
20. Complete the definition of Logarithm: For all positive numbers a, where a #1, and all positive numbers x.
Vladimir [108]

Answer:

A.

Step-by-step explanation:

y=loga(x) is just the same as x=a^y

6 0
3 years ago
What is the volume of the composite figure? Express the answer in terms of pie.
zhenek [66]

Answer:

3127 mm3

Step-by-step explanation:

3 0
3 years ago
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