Find f(-5) if f(n) = n3 + 3n2

10) 1 gallon of water for every inch of the fish's body length.
a) 2 1/2 inches long fish needs 2 1/2 gallon of water.
b) tank: l = 7 inches ; w = 5 inches; h = 7 ; volume = 7in * 5in * 7in = 245 in³
c) no. her fish tank is not large enough for the fish.
volume of 1 gallon of water is 231 in³, water needed is 2 1/2 gallon, so 5/2 * 231 in³ = 577.50 in³ volume.

11) volume = 7in * 3.5in * 1.75 in = 42.875 in³
weight of the brick = 0.1 pound per cubic inch ⇒ 42.875 in³ * 0.1 lb = 4.2875 pounds
weight of the gold bar = 0.7 pound per cubic inch ⇒ 42.875 in³ * 0.7 lb = 30.0125 pounds

12) l = 55cm ; w = 40cm ; h = 30 cm
volume = 55cm * 40cm * 30cm = 66,000 cm³

7 0

3 years ago

Scores at a local high school on the American College Testing (ACT) college entrance exam follow the normal distribution with a

san4es73 [151]

Answer:

a) The mean is 18 and the standard deviation is 1.79.

b) The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.

c) 0.2005 = 20.05% probability that a sample of 20 students has a mean score of 19.5 or more.

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, 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 of 18 and a standard deviation of 8.

This means that $\mu = 18, \sigma = 8$

Sample of 20:

This means that $n = 20, s = \frac{8}{\sqrt{20}} = 1.79$

(a) Calculate the mean and standard deviation of the sampling distribution of x¯.

By the Central Limit Theorem, the mean is 18 and the standard deviation is 1.79.

(b) Interpret the standard deviation from part (a).

The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.

(c) Find the probability that a sample of 20 students has a mean score of 19.5 or more.

This is 1 subtracted by the pvalue of Z when X = 19.5. So

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

By the Central Limit Theorem

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