370 College freshmen were interviewed. 200 were registered for an Advanced Math class. 270 were registered for an English class
220 were registered for a Sport Activity class. 100 were registered for both Math and English. 50 were registered for both Sport and English but not Math. 70 were registered for Math, Sport, and English.
a) How many signed up only for a Math class?
b) How many signed up for neither Math nor English?
c) How many signed up for an English class and at least one other class?
d) The cost for only one class per month is $100, for two - $150 and for three -$200. What is the total fee for all the students enrolled in classes?
a) How many signed up only for a Math class?
b) How many signed up for neither Math nor English?
c) How many signed up for an English class and at least one other class?
d) The cost for only one class per month is $100, for two - $150 and for three -$200. What is the total fee for all the students enrolled in classes?
1 answer:
Answer:
Step-by-step explanation:
To aid in understanding, draw three circles...
100 were registered for both Math and English.
50 were registered for both Sport and English but not Math.
70 were registered for Math, Sport, and English.
From here we will be able to calculate for those that signed up for only English class: Total number of students that signed up for english class
a. none signed up only for Maths (refer to attached document)
b. How many signed up for neither Math nor English meaning they signed up for only sports which is 70 from the venn diagram in the attachment.
c. How many signed up for an English class and at least one other class?
From the venn diagram:
we could have an English class and maths class - 100
we could also have an a English class and sports - 50
Thus total is 150.
d. What is the total fee for all the students enrolled in classes
From the diagram, 120 (english only and sport only) enrolled for only one class = 120 x $100 = $12,000
From the diagram, 180 (english and sport, maths and sport and english and maths) enrolled for two classes = 180 x $150 = $27,000
From the diagram, only 70 enrolled for the three classes = 70 x $200 = $14,000
Total fees = $12,000 + $27,000 + $14,000 = $53,000
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Answer:
The confidence interval for the mean is given by the following formula:
(1)
The 90% confidence interval for this case would be (38.01, 44.29) and is given.
The best interpretation for this case would be: We are 90% confident that the true average is between $ 38.01 and $ 44.29 .
And the best option would be:
The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29
Step-by-step explanation:
Assuming this complete question: Which statement gives a valid interpretation of the interval?
The store manager is 90% confident that the average amount spent by the 36 sampled customers is between S38.01 and $44.29.
There is a 90% chance that the mean amount spent by all customers is between S38.01 and $44.29.
There is a 90% chance that a randomly selected customer will spend between S38.01 and $44.29.
The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
The 90% confidence interval for this case would be (38.01, 44.29) and is given.
The best interpretation for this case would be: We are 90% confident that the true average is between $ 38.01 and $ 44.29 .
And the best option would be:
The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29