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3 years ago

15

i am begging for help. all of my points for the first to answer. The volume of a sphere is 3/4 x pi cm^3. what is the radios of

the sphere

1 answer:

horsena [70]3 years ago

3 0

volume of a sphere = 4/3 *pi * r^3

3/4 * pi = 4/3 *pi * r^3

divide each side by pi

3/4 = 4/3 * r^3

multiply each side by 3/4

3/4 * 3/4 = r^3

9/16 = r^3

take the cube root of each side

r = (9/16) ^ (1/3)

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3 years ago

At a Psychology final exam, the scores are normally distributed with a mean 73 points and a standard deviation of 10.6 points. T

USPshnik [31]

Answer:

The score that separates the lower 5% of the class from the rest of the class is 55.6.

Step-by-step explanation:

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.

In this question:

$\mu = 73, \sigma = 10.6$

Find the score that separates the lower 5% of the class from the rest of the class.

This score is the 5th percentile, which is X when Z has a pvalue of 0.05. So it is X when Z = -1.645.

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

$-1.645 = \frac{X - 73}{10.6}$

$X - 73 = -1.645*10.6$

$X = 55.6$

The score that separates the lower 5% of the class from the rest of the class is 55.6.

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3 years ago