Paul surely charges 75 dollars, and then he adds 40 dollars per hours. This means that the expression for the money he asks is
where is the amount of money and
is the number of hours.
Since can be at most 8, this is the case that generates the highest money, so if we plug
we have
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.