A perfect square is a number that has integer square root

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

2 years ago

Find the GCF

Kaylis [27]

Greatest Common Factor. let's go over that. GCF of 6 and 12 would be 6 because 6 goes into 6, 1 times and 6 goes into 12, 2 times. . and it is the largest. so first you see if the lower number can go directly into the higher number. So 28a^2 b^2 c^2, is made of 14abc× 2abc. so you can say 14abc goes into 28a2b2c2, 2abc times. therefore 14abc is the largest factor.

7 0

3 years ago

What is the answer for 25.2÷2.1 using showing my work

lilavasa [31]

Answer:

25.2

Step-by-step explanation:

2.1*12=25.2

use a calculator if you're allowed to show work that way, if not a simple way is

2.1*10=21

2.1*11=23.1

2.1*12 is equal to 2.1*10=21 because 2*12=24 and .1*12=1.2

7 0

3 years ago

Starting salaries of 90 college graduates who have taken a statistics course have a mean of $43,993 and a standard deviation of

Rufina [12.5K]

Answer: attached below

Step-by-step explanation:

5 0

3 years ago

Anyone good at trigonometry please help

s344n2d4d5 [400]

to find the vertical height

multiply the tangent of the angle by the horizontal distance

so tan(12) x 5 = 1.0628

rounded to nearest hundredth = 1.06 miles

6 0

2 years ago