Download Normal Probability Distribution with TI 83 (students)

Normal Probability Distribution with
TI 83/84 calculator
The Normal Distribution functions:
#1: normalpdf pdf = Probability Density Function
This function returns the probability of a single value of the random variable x. Use
this to graph a normal curve. Using this function returns the y-coordinates of the
normal curve.
Syntax: normalpdf (x, mean, standard deviation)
#2: normalcdf cdf = Cumulative Distribution Function
This function returns the cumulative probability from zero up to some input value of
the random variable x. Technically, it returns the percentage of area under a
continuous distribution curve from negative infinity to the x. You can, however, set
the lower bound.
Syntax: normalcdf (lower bound, upper bound, mean, standard deviation)
#3: invNorm( inv = Inverse Normal Probability Distribution Function
This function returns the x-value given the probability region to the left of the xvalue.
(0 < area < 1 must be true.) The inverse normal probability distribution function will
find the precise value at a given percent based upon the mean and standard deviation.
Syntax: invNorm (probability, mean, standard deviation)
Example 1:
Given a normal distribution of values for which the mean is 70 and the standard
deviation is 4.5. Find:
a) the probability that a value is between 65 and 80, inclusive.
b) the probability that a value is greater than or equal to 75.
c) the probability that a value is less than 62.
d) the 90th percentile for this distribution.
(answers will be rounded to the nearest thousandth)
1a: Find the probability that a value is between 65 and 80,
inclusive. (This is accomplished by finding the probability of the
cumulative interval from 65 to 80.)
Syntax:normalcdf(lower bound, upper bound, mean, standard deviation)
Answer: The probability is
1b: Find the probability that a value is greater than or
equal to 75.
(The upper boundary in this problem will be positive infinity. The
largest value the calculator can handle is 1 x 1099. Type 1 EE 99.
Enter the EE by pressing 2nd, comma -- only one E will show on
the screen.)
Answer: The probability is
1c: Find the probability that a value is less than 62.
(The lower boundary in this problem will be negative infinity. The
smallest value the calculator can handle is -1 x 1099. Type -1 EE
99. Enter the EE by pressing 2nd, comma -- only one E will show
on the screen.)
Answer: The probability is
1d: Find the 90th percentile for this distribution.
(Given a probability region to the left of a value (i.e., a percentile),
determine the value using invNorm.)
Answer: The x-value is
Example 2: Graph and examine a situation where the mean score is 46 and the standard
deviation is 8.5 for a normally distributed set of data.
Go to Y= .
1.
Adjust the window.
GRAPH.
Practice and Homework (Independenteven # and HW# odd)
The amount of mustard dispensed from a machine at The
Hotdog Emporium is normally distributed with a mean of
0.9 ounce and a standard deviation of 0.1 ounce. If the
machine is used 500 times, approximately how many times
will it be expected to dispense 1 or more ounces of
mustard.
Choose:
5
16
80
100
2.
Professor Halen has 184 students in his college
mathematics lecture class. The scores on the midterm
exam are normally distributed with a mean of 72.3
and a standard deviation of 8.9. How many students
in the class can be expected to receive a score
between 82 and 90? Express answer to the nearest
student.
3.
A machine is used to fill soda bottles. The amount of soda
dispensed into each bottle varies slightly. Suppose the
amount of soda dispensed into the bottles is normally
distributed. If at least 99% of the bottles must have
between 585 and 595 milliliters of soda, find the greatest
standard deviation, to the nearest hundredth, that can be
allowed.
4.
Residents of upstate New York are accustomed to large
amounts of snow with snowfalls often exceeding 6
inches in one day. In one city, such snowfalls were
recorded for two seasons and are as follows (in inches):
8.6, 9.5, 14.1, 11.5, 7.0, 8.4, 9.0, 6.7, 21.5, 7.7, 6.8, 6.1,
8.5, 14.4, 6.1, 8.0, 9.2, 7.1
What are the mean and the population standard deviation
for this data, to the nearest hundredth?
5.
Neesha's scores in Chemistry this semester were rather
inconsistent: 100, 85, 55, 95, 75, 100.
For this population, how many scores are within one standard
deviation of the mean?
6.
Battery lifetime is normally distributed for large samples.
The mean lifetime is 500 days and the standard deviation is
61 days. To the nearest percent, what percent of batteries
have lifetimes longer than 561 days?
7. The number of children of each of the first 41
United States presidents is given in the
accompanying table. For this population,
determine the mean and the standard
deviation to the nearest tenth.
How many of these presidents fall within one
standard deviation of the mean?
8.
From 1984 to 1995, the winning scores for a golf
tournament were 276, 279, 279, 277, 278, 278, 280, 282,
285, 272, 279, and 278. Using the standard deviation for
this sample, Sx, find the percent of these winning scores
that fall within one standard deviation of the mean.
9.
A shoe manufacturer collected data regarding men's shoe
sizes and found that the distribution of sizes exactly fits
the normal curve. If the mean shoe size is 11 and the
standard deviation is 1.5, find:
a. the probability that a man's shoe size is greater than or
equal to 11.
b. the probability that a man's shoe size is greater than or
equal to 12.5.
c.
10.
Five hundred values are normally distributed with a mean
of 125 and a standard deviation of 10.
a. What percent of the values lies in the interval 115 - 135,
to the nearest percent?
b. What percent of the values is in the interval 100 - 150,
to the nearest percent?
c. What interval about the mean includes 95% of the data?
d. What interval about the mean includes 50% of the data?
11.
A group of 625 students has a mean age of 15.8 years with a
standard deviation of 0.6 years. The ages are normally
distributed. How many students are younger than 16.2
years? Express answer to the nearest student?