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Y_Kistochka [10]
3 years ago
10

2. An apple has a diameter of 8 cm. An orange has a diameter of 11 cm. Determine how many times greater the volume of the orange

is compared to that of the apple. Round to the nearest hundredth (treat both fruits as spheres)
Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
6 0

Answer:

Volume of a sphere = 4πr³

Volume of Orange = 4/3×22/7×4³=268.1904, Volume of Apple = 4/3× 22/7×(11/2)³=697.1904 Now, Volume of Orange - Volume of Apple, 697.1904-268.1904 = 429.0000,. Therefore, the answer is 429.00

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31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

Step-by-step explanation:

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

Normal probability distribution

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

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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.

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In this question, we have that:

\mu = 270, \sigma = 90, n = 18, s = \frac{90}{\sqrt{18}} = 21.2

What is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days?

This is the pvalue of Z when X = 260. So

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

By the Central Limit Theorem

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

Z = \frac{260 - 270}{21.2}

Z = -0.47

Z = -0.47 has a pvalue of 0.3192.

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