Bob, a weak swimmer, ignored warning signs in a recreational swimming area and went into deep water. He soon grew tired and real
1 answer:
You might be interested in
Answer:
Explanation:
Data given and notation
represent the sample mean
represent the standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to determine if the mean is lower than 5600, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
3)
Jorge Rodrigues annual salary is:
We know that 1 year consists of 12 months, so the gross wage per month can be obtained by dividing the annual salary by 12:
1 year also contains 52 weeks, so the gross wage per week is obtained by dividing the annual salary by 52:
Finally, 1 year contains 26 bi-week periods, so the gross wage per bi-week period is:
4)
In this part, we know that Lexi's salary per month is:
We know that 1 year consists of 12 months: therefore, the annual salary contains 12 monthly salary, so we can write
where
n = 12 is the number of months
S is the annual salary
Substituting s, we find:
5)
Here the Monthly salary of Ryo is
So her annual salary is the monthly salary multiplied by 12:
Then Ryo has been offered a raise of $250 per month, so her new salary per month will be
Therefore, her new annual salary will be
So, the amount that Ryo will earn more per year is:
6)
Being paid salary means that we are paid with a fixed regular payment, usually paid every month.
Being paid by hourly rate instead means that we are paid a fixed amount for every hour of work: therefore, the total monthly salary will depend on the number of hours of work.
Therefore, the main advantages/disadvantages are the following:
- Advantage of being paid salary: the payment is fixed, therefore it is independent on the number of hours worked - so even if one month we work less hours, we still receive the same pay
- Disadvantages: the salary is fixed and cannot be increased by working more - in fact, in the hourly payment, by working more hours it is possible to earn more.
7)
In this problem, the amount of the check in the restaurant is
The customer decides to leave a 20% tip, which corresponds to of the amount of check.
Therefore, we can write the amount of the tip left as
Simplifying, we get
And by substituting c = 340, we find the tip left:
8)
In this problem, Sandra is paid per day.
Her pay per day is
Which means that she is paid 95 dollars per day.
In this month, Sandra has worked for
n = 22 days
Therefore her total earning for this month will be
and substituting n = 22 and d = 95, we find:
9)
First of all, we have to find the total number of pieces produced by summing the number of pieces produced each day.
For Zinke, the total number of pieces produced is:
n = 54 + 55 + 59 + 62+ 60 = 290
The price per piece produced is
p = $1.60
Therefore, the gross pay is equal to the number of pieces times the price per piece:
Then we have to repeat the exercise for Bello. The total number of pieces produced is:
n = 24 + 28 + 30 + 31 + 27 = 140
The price per piece is
p = $2.80
So, the gross pay is:
10)
Here the fare for the whole drive was
f = $19.30
However, Steve gave the driver a total of 20$. This means that the tip gave by Steve to the driver is
Here we are asked to determine if the tip is adequate, generous or not enough. In order to evaluate this, we have to calculate what is the tip in % with respect to the fare.
It is:
The tip is 3.6% of the fare: therefore, the tip is not enough (an adequate tip can be considered between 10 and 20 %).