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Among all monthly bills from a certain credit card company, the mean amount billed was $465 and the standard deviation was $300.

Fynjy0 [20]

Answer:

0.02% probability that the average amount billed on the sample bills is greater than $500.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Normal probability distribution

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 problem, we have that:

$\mu = 465, \sigma = 300, n = 900, s = \frac{300}{\sqrt{900}} = 10$ .

What is the probability that the average amount billed on the sample bills is greater than $500?

This probability is 1 subtracted by the pvalue of Z when $X = 500$ . So

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

$Z = \frac{500 - 465}{10}$

$Z = 3.5$

$Z = 3.5$ has a pvalue of 0.9998.

So there is a 1-0.9998 = 0.0002 = 0.02% probability that the average amount billed on the sample bills is greater than $500.

8 0

3 years ago

True or false? Rates can be adjusted for different time periods. If you know how many parts can be made in an hour, then you can

julsineya [31]

Answer:

True

Step-by-step explanation:

The whole point of units conversion is to take a value expressed in one set of units (parts per hour) and translate it to a different set of units (parts per week). The rate does not have to involve time.

The statement is TRUE.

3 0

3 years ago

Llana [10]

It shows that the values of the mileages are close to 24 mpg. Hence statistics refes 24 as the mean.

Mean is one of the measure of dispersion and is the avearage of a set of data.

According to the question, the magazine reports that the most common gas mileage was 24 mpg. This shows that reports have published several gas mileages for cars and truck and the average of this mileage is 24mpg

It shows that the values of the mileages are close to 24 mpg. Hence statistics refes 24 as the mean.

Learn more on mean here: brainly.com/question/14532771

#SPJ1

4 0

2 years ago

In your garden, sandy soil can be corrected by adding what?

Alex17521 [72]

Maybe by adding water

4 0

3 years ago

50 Points What is the value of r? 6.4r−5.9r=−3.25 Question 1 options: A -6.5 B 6.5 C -3

Oliga [24]