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1. Mr. Spock sees a Gorn. He says that the Gorn is in the 95.99th percentile. If the heights of Gorns are normally distributed with a mean of 200 cm and a standard deviation of 5 cm. How tall is the Gorn? Don't round!
2. The Tholians are trying to capture Enterprise by creating a 'space web'

The width of the square gaps or holes in the web is normally distributed with a mean width of 400 feet and a standard deviation of 16 feet. Enterprise requires a gap of at least 422 feet to escape.

A.) What is the probability that a gap will be 420 feet or wider?

B.)If there are 10,000 gaps in a web, approximately how many will Enterprise be able to pass through?

3. USS Enterprise has had a refit and has had its main phasers upgraded.

Previously, the average power in a phaser blast was 1.75 terawatts with a standard deviation of 0.12 terawatts. After a series of 16 test firings, the average power of the test blasts is 1.8 terawatts.Conduct all tests at the 95% level of confidence.

Two-Tailed Test.

A.) State the critical value for 'z'.

B.) State the Null and Alternative hypotheses.

C.) Construct a 95% confidence interval estimator for the true mean power of the phasers. Provide an interpretation of this interval.

D.) Conduct the two-tailed test and state your conclusion with a reason!

E.) Identify the error that might have occurred and which error is impossible.

One-Tailed test and p-value.

F.) Identify the critical value of 'z'.

G.) State the Null and Alternative hypotheses.

H.) Conduct the One-Tailed test, and state your conclusion and why!

I.) Identify the error that may have occurred and which is impossible.

J.) Find the p-value of this test. Provide an interpretation. Does the p-value support the one-tailed test?

Separate Question (given picture)

USS Enterprise must travel to Earth using a path through this grid. A probe called Nomad is located where the small ellipse is (at a lattice point on the grid). If the ship's navigational computer randomly selects a path through the grid, what is the probability that Enterprise will encounter Nomad on the way to Earth?