Question

1. There are two machines available for cutting corks intended

for use in wine bottles. The first produces corks with diameters

that are normally distributed with mean 3 cm and standard

deviation .1 cm. The second machine produces corks

with diameters that have a normal distribution with mean

3.04 cm and standard deviation .02 cm. Acceptable corks

have diameters between 2.9 cm and 3.1 cm. Which machine

is more likely to produce an acceptable cork?

2. The weight distribution of parcels sent in a certain manner

is normal with mean value 12 lb and standard deviation

3.5 lb. The parcel service wishes to establish a weight value

c beyond which there will be a surcharge. What value of c

is such that 99% of all parcels are at least 1 lb under the surcharge

weight?

9. Let X denote the distance (m) that an animal moves from its

birth site to the first territorial vacancy it encounters.

Suppose that for banner-tailed kangaroo rats, X has an exponential

distribution with parameter lamda=.01386 (as suggested

in the article “Competition and Dispersal from

Multiple Nests,” Ecology, 1997: 873–883). What is the probability that the distance is at most

100 m? At most 200 m? Between 100 and 200 m?

10. Find the z value to the right of the mean so that

a. 54.78% of the area under the distribution curve lies

to the left of it.

b. 69.85% of the area under the distribution curve lies

to the left of it.

c. 88.10% of the area under the distribution curve lies

to the left of it.

11. The average annual salary for all

U.S. teachers is $47,750. Assume that the distribution is

normal and the standard deviation is $5680. Find the

probability that a randomly selected teacher earns

a. Between $35,000 and $45,000 a year

b. More than $40,000 a year

c. If you were applying for a teaching position and

were offered $31,000 a year, how would you feel

(based on this information)?

12.The national average SAT score (for

Verbal and Math) is 1028. If we assume a normal

distribution with standard deviation 92, what is the 90th percentile

score? What is the probability that a randomly selected

score exceeds 1200?

13. The average credit card debt for

college seniors is $3262. If the debt is normally

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

14. The average waiting time to be

seated for dinner at a popular restaurant is 23.5 minutes,

with a standard deviation of 3.6 minutes. Assume the

variable is normally distributed. When a patron arrives

at the restaurant for dinner, find the probability that the

patron will have to wait the following time.

a. Between 15 and 22 minutes

b. Less than 18 minutes or more than 25 minutes

c. Is it likely that a person will be seated in less than

15 minutes?

Answer 1

1. There are two machines available for cutting corks intended

for use in wine bottles. The first produces corks with diameters

that are normally distributed with mean 3 cm and standard

deviation .1 cm. The second machine produces corks

with diameters that have a normal distribution with mean

3.04 cm and standard deviation .02 cm. Acceptable corks

have diameters between 2.9 cm and 3.1 cm. Which machine

is more likely to produce an acceptable cork?

2. The weight distribution of parcels sent in a certain manner

is normal with mean value 12 lb and standard deviation

3.5 lb. The parcel service wishes to establish a weight value

c beyond which there will be a surcharge. What value of c

is such that 99% of all parcels are at least 1 lb under the surcharge

weight?

10. ind the z value to the right of the mean so that

a. 54.78% of the area under the distribution curve lies

to the left of it.

b. 69.85% of the area under the distribution curve lies

to the left of it.

c. 88.10% of the area under the distribution curve lies

to the left of it.

13. The average credit card debt for

college seniors is $3262. If the debt is normally

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