Download Example #1

Section 6-2 Example Problems
Uniform Distribution:
Example #1:
A statistics professor plans classes so carefully that the lengths of
her classes are uniformly distributed between 50.0 min and 52.0 min. That is, any
time between 50.0 min and 52.0 min is possible, and all of the possible values are
equally likely. If we randomly select one of her classes and let x be the random
variable representing the length of that class, then x has a distribution that can be
graphed. Develop the graph:
Example #2:
Kim, who has developed a habit of living on the edge, has scheduled
a job interview immediately following her statistics class. If the class runs longer
than 51.5 minutes, she will be late for the job interview. Use your graph from
Example #1 to find the probability that a randomly selected class will last longer than
51.5 minutes.
Standard Normal Distribution – Find Probability
Example #3:
The Precision Scientific Instrument Company manufactures
thermometers that are supposed to give readings of 0˚C at the freezing point of water.
Tests on a large sample of these instruments reveal that at the freezing point of
water, some thermometers give readings below 0˚ and some give readings above 0˚.
Assume that the mean reading is 0˚C and the standard deviation of the readings is
1.00˚C. Also assume that the readings are normally distributed. If one thermometer
is randomly selected, find the probability that, at the freezing point of water, the
reading is less than 1.58˚C.
Example #4:
Using the thermometers from the preceding example, find the
probability of randomly selecting one thermometer that reads above -1.23˚.
Example #5:
Once again, make a random selection from the same sample of
thermometers. Find the probability that the chosen thermometer reads between –
2.00˚ and 1.50˚.
Standard Normal Distribution – Find z-score
Example #6:
Using the same thermometers as before, find the temperature
corresponding to P95 , the 95th percentile. That is, find the temperature separating the
bottom 95% from the top5%.
Example #7:
Using the same thermometers, find the temperature separating the
bottom 2.5% and the top 2.5%.