1.

X ~ N(60,9). Suppose that you form random samples of 25 from this distribution. Letbe the random variable of averages. Let X be the random variable of sums. Round all answers to two decimal places.

A.~ N(,)

B. P(<60) =

C. Find the 20thpercentile for thedistribution.

D. P(58<<61)=

E. Q1 for thedistribution =

F. X ~ N(,)

G. P( X < 1450) =

2.

Each sweat shop worker at a computer factory can put together 4 computers per hour on average with a standard deviation of 0.8 computers. 20 workers are randomly selected to work the next shift at the factory. Round all answers to two decimal places and assume a normal distribution.

A.~ N(,)

B. For the 20 workers, find the probability that their average number of computers put together per hour is between 3 and 5.

C. If one randomly selected worker is observed, find the probability that this worker will put together between 3 and 5 computers per hour.

D. Then the distribution of the total number of computers that 20 randomly selected workers can put together per hour is N(,)

E. Find the probability that a 20 person shift will put together between 75 and 85 computers per hour.

F. The top 5% of all 20 person shifts will receive an extra day of vacation this year. What is the fewest number of computers per hour a team must put together in order to receive the extra day of vacation?computers.

3.

Suppose that the age that children learn to walk is normally distributed with mean 12 months and standard deviation 1 month. 19 randomly selected people were asked what age they learned to walk. Round all answers to two decimal places.

A.~ N(,)

B. For the 19 people, find the probability that the average age that they learned to walk is between 11.5 and 12.5 months old.

C. What is the probability that one randomly selected person learned to walk when they were between 11.5 and 12.5 months old?

D. Find the IQR for the average first time walking age for groups of 19 people.

Q1 =

Q3 =

IQR:

4.

The average number of miles (in thousands) that a car's tire will function before needing replacement is 68 and the standard deviation is 15. Suppose that 9 randomly selected tires are tested. Round all answers to two decimal places and assume a normal distribution.

A.~ N(,)

B. For the 9 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 65 and 75 .

C. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 65 and 75 .