What property does the following equation show? 5+7+9=7+5+9
2 answers:
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Answer:
Average price, excluding taxes, for each CD is <u>10.20</u>.
Step-by-step explanation:
Given:
Cost of first 5 CDs,
Cost of each additional CD = 15.00
Now, cost of 10 additional CDs is the product of cost of one CD and total number of additional CDs. Therefore,
Cost of 10 additional CDs is,
Now, total CDs purchased by Jana are,
Total cost of the 15 CDs purchased is given as:
Now, average price, excluding taxes, for each CD is given as:
Therefore, the average price, excluding taxes, for each CD is 10.20.
Answer:
a) 68% probability that the sample mean will be within ±5 of the population mean.
b) 95% probability that the sample mean will be within ±10 of the population mean.
Step-by-step explanation:
To solve this problem, we have to understand the Empirical Rule and the Central Limit Theorem
Empirical Rule
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
Mean:
Standard deviation of the population:
Size of the sample:
Standard deviation for the sample mean:
a.What is the probability that the sample mean will be within ±5 of the population mean?
5 is one standard deviation from the mean.
By the Empirical Rule, 68% probability that the sample mean will be within ±5 of the population mean.
b.What is the probability that the sample mean will be within ±10 of the population mean?
10 is two standard deviations from the mean
By the Empirical Rule, 95% probability that the sample mean will be within ±10 of the population mean.