I need explanations

Information

A factory makes parts for laptop computers, including screws.

The screws are required to have the right length. The lengths

of the screws obey a normal distribution with

mean =4.25 and standard

deviation =0.022.

Please use this information for the

next questions.

A technician randomly selects a screw, measures its length,

and calculates the z-score of the screw to be 1.7. Interpret this

z-score.

Question options:

The screw is longer than 1.7% of all the screws made by the factory.

The screw is 1.7 standard deviations longer than average.

The screw is 1.7mm too long.

The screw is 1.7mm long.

Question

A technician randomly selects another screw and finds the zscore

of its length to be -2.7. Which one of the following would

be a valid interpretation of this z-score?

The screw is unusually short.

The screw is unusually long.

The screw is neither unusually short nor unusually long.

More information is needed before any valid conclusion can be drawn.

Question

A randomly selected screw is 4.24mm long. Calculate the zscore

of its length.

Answer:

Question

Company policy at the factory requires screws to be between

4.20mm and 4.30mm. Calculate the probability that a

randomly selected screw meets this requirement.

Answer:

Calculate the 95th percentile of screw lengths.

Answer:

Suppose a simple random sample of n = 20 screws is

selected. Calculate the probability that their mean length is

less than 4.26 millimeters.

Answer:

Question

Again, suppose a simple random sample of n = 20 screws is

selected. Calculate the probability that their mean length is

greater than 4.265 millimeters.

Answer:

Question

Once again, suppose a simple random sample of n = 20

screws is selected. Calculate the probability that their mean

length is between 4.243mm and 4.257mm. Answer: