There are two machines available for cutting corksintended
for use in wine bottles. The first produces corks withdiameters
that are normally distributed with mean 3 cm andstandard
deviation .1 cm. The second machine producescorks
with diameters that have a normal distribution withmean
3.04 cm and standard deviation .02 cm. Acceptablecorks
have diameters between 2.9 cm and 3.1 cm. Whichmachine
is more likely to produce an acceptablecork?
The weight distribution of parcels sent in a certainmanner
is normal with mean value 12 lb and standarddeviation
3.5 lb. The parcel service wishes to establish a weightvalue
c beyond which there will be a surcharge. What value ofc
is such that 99% of all parcels are at least 1 lb underthe surcharge
weight?
9. Let X denote the distance (m) that an animal movesfrom its
birth site to the first territorial vacancy itencounters.
Suppose that for banner-tailed kangaroo rats, X has anexponential
distribution with parameter lamda=.01386 (assuggested
in the article “Competition and Dispersalfrom
Multiple Nests,” Ecology, 1997: 873–883). What is theprobability that the distance is at most
100 m? At most 200 m? Between 100 and 200m?
Find the z value to the right of the mean sothat
a. 54.78% of the area under the distribution curvelies
to the left of it.
b. 69.85% of the area under the distribution curvelies
to the left of it.
c. 88.10% of the area under the distribution curvelies
to the left of it.
11. The average annual salary for all
U.S. teachers is $47,750. Assume that the distributionis
normal and the standard deviation is $5680. Findthe
probability that a randomly selected teacherearns
a. Between $35,000 and $45,000 a year
b. More than $40,000 a year
c. If you were applying for a teaching positionand
were offered $31,000 a year, how would youfeel
(based on this information)?
12.The national average SAT score (for
Verbal and Math) is 1028. If we assume anormal
distribution with standard deviation 92, what is the90th percentile
score? What is the probability that a randomlyselected
score exceeds 1200?
The average credit card debt for
college seniors is $3262. If the debt isnormally
distributed with a standard deviation of $1100,find
these probabilities.
a. That the senior owes at least $1000
b. That the senior owes more than $4000
c. That the senior owes between $3000 and$4000
The average waiting time to be
seated for dinner at a popular restaurant is 23.5minutes,
with a standard deviation of 3.6 minutes. Assumethe
variable is normally distributed. When a patronarrives
at the restaurant for dinner, find the probability thatthe
patron will have to wait the followingtime.
a. Between 15 and 22 minutes
b. Less than 18 minutes or more than 25minutes
c. Is it likely that a person will be seated in lessthan
15 minutes?
