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1 year ago

When Nabhitha goes bowling, her scores are normally distributed with a mean of 115

Mathematics

1 answer:

frutty [35]1 year ago

7 0

Answer:

By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232Step-by-step explanation:The Empirical Rule states that, for a normally distributed random variable:68% of the measures are within 1 standard deviation of the mean.95% of the measures are within 2 standard deviation of the mean.99.7% of the measures are within 3 standard deviations of the mean.In this problem, we have that:Mean = 190Standard deviation = 14Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?148 = 190 - 3*14So 148 is 3 standard deviations below the mean.232 = 190 + 3*14So 232 is 3 standard deviations above the meanBy the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232

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Nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?

NemiM [27]

Answer:

72°

Step-by-step explanation:

The cookie has a shape of a circle. A circle is the locus of a point such that its distance from a point (center) is always the same. The sum of angles around the circle center is 360°.

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3 years ago

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The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.8, 15.6, 15.1, 15.2, 15.1, 15.5, 15.9, 15.5. C

Bingel [31]

Answer:

The required 97.5% confidence interval is

$\text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\\text {CI} = 15.5 \pm 2.8412\cdot \frac{0.31}{\sqrt{8} } \\\\\text {CI} = 15.5 \pm 2.8412\cdot 0.1096\\\\\text {CI} = 15.5 \pm 0.311\\\\\text {CI} = 15.5 - 0.311, \: 15.5 + 0.311\\\\\text {CI} = (15.19, \: 15.81)\\\\$

Therefore, we are 97.5% confident that the actual mean amount of juice in all such bottles is within the range of 15.19 to 15.81 ounces

Step-by-step explanation:

The amounts (in ounces) of juice in eight randomly selected juice bottles are:

15.8, 15.6, 15.1, 15.2, 15.1, 15.5, 15.9, 15.5

Let us first compute the mean and standard deviation of the given data.

Using Excel,

=AVERAGE(number1, number2,....)

The mean is found to be

$\bar{x} = 15.5$

=STDEV(number1, number2,....)

The standard deviation is found to be

$s = 0.31$

The confidence interval for the mean amount of juice in all such bottles is given by

$$ \text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\\\\$

Where $\bar{x}$ is the sample mean, n is the samplesize, s is the sample standard deviation and $t_{\alpha/2}$ is the t-score corresponding to a 97.5% confidence level.