Download Math 4 - Practice with Sample Means #2

Math 4 - Practice with Sample Means #2
1.
Name_________________________
Since 2000, the duration of every movie released in the United States can be placed
into a data set that is normally distributed. The mean of this population is 111 minutes,
and the standard deviation is 14 minutes. Suppose the 8 movies that are currently at
Masters Cinemas serve as a random sample from this population. What is the
probability the average duration of these 8 movies is greater than 120 minutes (2 hrs)?
Round your answer to four decimal places.
For Questions 2-4, consider the following data set: {3, 5, 7, 9, 11}.
2.
What is the sampling distribution of the sample means for all samples of size 2 from
this data set?
3.
What is the mean of all of the sample means of size 2 from this data set?
4.
The formula,  x 

, cannot be used in order to find the standard deviation
n
of the sampling distribution of the sample means. Why not?
For Questions 5-7, consider a population of 100 data values in which samples of a size greater
than 1 but less than 99 are taken.
5.
True or False: The sampling distribution of the sample means will have more data
values than the original population.
6.
True or False: The standard deviation of the sampling distribution of the sample means
will be greater than the standard deviation of the original population.
7.
True or False: The mean of the sampling distribution of the sample means will be
different than the mean of the population.
For Questions 8-10, consider the following: the final grades in a college Spanish class for all 600
students enrolled have a normal distribution, with a mean of 77 and a standard deviation of 10.
8.
In order to have a grade at which only 20% of the enrolled students scored higher than
you, what must your final grade be? Round your answer to the one decimal place.
9.
What percentage of students failed the course (scored a "69" or lower)? Round your
answer to two decimal places.
10.
What percentage of students made a C (scored between a "73" and a "79")? Round
your answer to two decimal places.
In all 10-minute games of Halo 2 online for the original X-Box, the number of kills per player is
recorded in a data set. This data set has a normal distribution with a mean of 13.2, and a
standard deviation of 6. Use this information to answer Questions 11 & 12.
11.
Suppose five online players are selected randomly. What is the probability that their
mean number of kills is greater than 10? Round your answer to four decimal places.
12.
Tron brags, "Man, I am killin' it. The game I just played ranked me in the 92 nd
percentile!" Approximately how many kills did he have in this game? Round your
answer to the nearest whole number.
13.
Sara is thinking of placing her money in stocks, but she knows very little about the
market. So, she decides she will randomly select stocks and pour her money into them.
If Sara's objective is to minimize risk, even at the sake of lowering the potential for
huge profit, which of the following should you recommend: picking one stock and
placing all money into it, OR dividing her money evenly amongst ten stocks?
At all fast food restaurants in America, suppose the number of calories of every menu item is
placed in a data set that is normally distributed with a mean of 475 calories and a standard
deviation of 85 calories. Use this information to answer Questions 14 & 15.
14.
What percentage of menu items at fast food restaurants have a number of calories
that is greater than 600? Round to two decimal places.
15.
Suppose three fast food items are chosen randomly. What is the probability the
average number of calories in the items is less than 450 calories? Round to four
decimal places.
1. 0.0344
2. {4, 5, 6, 6, 7, 7, 8, 8, 9, 10} 3. 7
4. Because the original population is not normally distributed, AND because the size of the
population is not at least ten times the size of the sample.
5. True
6. False
7. False
8. 85.4 (or 85.5) 9. 21.19%
10. 23.47%
11. 0.8830
12. 22
13. dividing her money evenly amongst ten stocks
14. 7.08%
15. 0.3050