Probability and standard deviation

A software distributor is considering whether to purchase a batch of
20,000 3.5” floppy disks at a flea market auction for 4 cents each.
The disks were originally guaranteed by the manufacture to be only 5%
defective, but no returns are allowed at this price. Before rushing to
make a payment, the distributor decided to select a random sample of 20
disks to investigate the quality claim anyway. After all, too many
defective disks (over 10%) rule out the purchase, irrespective of the
bargain price.

a. What is the probability that no defective disks are found in the
sample?

b. What is the probability that 3 or more defective disks are found in
the sample?

c. What is the probability that less than 2 defective disks are found in
the sample?

d. What is the probability that all the disks in the sample are
defective?

e. If 3 defective disks are found in the sample, what can you conclude
about the original guarantee?

Suppose that 40% of a population have blue eyes. The number of people
with blue eyes in a sample of 600 has a binomial distribution. The mean
of the distribution is 240, and the standard deviation is 12. True or
False

The average speed of all vehicles on a highway is 65 and the standard
deviation is 4. If the speeds are normally distributed, a car traveling
73 has a z-score of 2. True or False

If P(X>x)=0.34 and P(X=x)=0.10, thenP(<_x)=0.56 true or flase

A sample of 25 electric motors is taken from a large lot. The average
current drawn by each motor at rated speed and RPM is 7.65 amps. The
standard deviation of the sample is 0.15 amps. If the motor are rated on
the stamped nameplate as drawing 7.5 amps,what is the z-score for this
sample?