Download Normal Curve with excel

1
The Normal Curve and Excel
The 68-95-99.7 rule is a nice beginning from which to explore the normal curve.
It would be greatly limiting if we could only work with z-scores of 1; 2 and
3. Fortunately, technology allows us to work with any z-score in any normal
distribution.
Excel has two basic types of normal curve commands; …nd the percentage
of data below a certain value or …nd a value with a certain percentage of data
below it. Both functions are found from the formulas tab under more functions
and then selecting statistical.
2
NORMDIST
The NORMDIST command in Excel 2007 will compute the percentage of data
that falls below a value x in a normal distribution.
Problem 1 On a particular track team mile running times follow a normal
distribution with a mean of 8.5 minutes and a standard deviation of 1.2 minutes.
What percentage of the track team runs a mile in under 7 minutes?
To answer this question select the NORMDIST command from the Excel
menu. You will see the following menu pop up.
1
In this problem …ll in x = 7, the Mean is 8.5 and Standard_dev is 1.2. Type
1 into the Cumulative box.
2
Hit OK and we get the answer 0:105649774
10:5%.
Problem 2 On a particular track team mile running times follow a normal
distribution with a mean of 8.5 minutes and a standard deviation of 1.2 minutes.
What percentage of the track team runs a mile in under 7 minutes? By the
preceding calculation 10.5% of the track team can run a mile in under 7 minutes.
Problem 3 On a particular track team mile running times follow a normal
distribution with a mean of 8.5 minutes and a standard deviation of 1.2 minutes.
What percentage of the track team runs a mile in over 7 minutes?
Problem 4 On a particular track team mile running times follow a normal
distribution with a mean of 8.5 minutes and a standard deviation of 1.2 minutes.
What percentage of the track team runs a mile in between 8 and 9.3 minutes?
3
3
NORMINV
What if we want to reverse the question? What if we want to …nd a value based
on a percentage such as when computing a percentile score? In this case we
use the NORMINV command.
Problem 5 On a particular track team mile running times follow a normal
distribution with a mean of 8.5 minutes and a standard deviation of 1.2 minutes.
What time separates the fastest 10% of the runners from the rest of the team?
4
Click OK and the result is 6:962138121. So the fastest 10% of the team can
run a mile in under 7 minutes.
Problem 6 On a particular track team mile running times follow a normal
distribution with a mean of 8.5 minutes and a standard deviation of 1.2 minutes.
What time separates the fastest 15% of the runners from the rest of the team?
Problem 7 On a particular track team mile running times follow a normal
distribution with a mean of 8.5 minutes and a standard deviation of 1.2 minutes.
The slowest 20% of all runners will be cut from the team. How fast of a mile
does one need to run in order to stay on the team?
4
Exercises
Clark: Section 6.4: Do problems 3, 4, 5, 8, 9
1. The average length (http://wiki.answers.com/Q/How_long_does_the_average_baseball_game_last)
of a MLB game follows a normal distribution with a mean of 174 minutes
and a standard deviation of 28 minutes.
i. What percentage of games are …nished in under 2.5 hours?
ii. Julia wants at least two and half hours of entertainment from a baseball
game but gets bored if the game takes more than three and a half hours.
What percentage of baseball games make Julia happy?
iii. The longest 10% of all games require a minimum of how many minutes
to play?
iv. A professional baseball team plays 162 games in a season. Based
solely on the data given, how many Atlanta Braves games do you expect
to last at least 3 hours? What variables might change the length of a
game for a particular team?
v. It is a stretch to claim game times follow a normal distribution. Why?
2. Assume combined points scored by both teams in an NBA games follows
a normal distribution with an average of 184.3 points and a standard
deviation of 23.8 points.
i. What percentage of games have a combined score of at least 170 points?
ii. What percentage of games have a combined score of at least 200 points?
iii. Based on the work from (ii), in thr 82 game season, how many Atlanta
Hawks’games yield a combined score of at least 200 points? Discuss (3-4
5
sentences) a concern you might have with this prediction.
iv. Without doing the computations, which is larger
A) the percentage of games that have a combined score of between 180
points and 190 points
or
B) the percentage of games that have a combined score of between 170
points and 200 points?
Explain.
3. In 1980, the video game Pac-Man was released and became an international phenomenon. At a particular arcade, people who played Pac-Man
spent an average of $2.35 with a standard deviation of 60 cents. Assume
money spent follows a normal distribution.
i. What percentage of players spent between $1 and $2?
ii. What percentage of players spent more than $4?
iii. At least how much money was spent by players who spent the top
25%?
iv. Do you think there is a correlation between money spent at Pac-Man
and time playing Pac-Man? Explain.
v. What is the average and standard deviation of number of games played?
6