Hi, please answer all the questions and show work. I need it before 8:20pm. Thank you.

1. Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals).

A. P(z -1.70)

B. P(z -1.70)

2. The duration of computer repair time at a local shop, is uniformly distributed between 25 minutes and 50 minutes. What is the probability that a repair takes between 30 minutes and 42 minutes? Do not round the values.

A. First find the density f(x).

B. The probability:

C. Find the mean repair time:

3. Find the z-score for which the area to its left is approximately 0.52.

z =

4. Television viewing reached a new high when the global information and measurement company reported a mean daily viewing time of 8.35 hours per household.

Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household.

What is the probability that a household views television less than 7 hours?

First find the z-score.

A. Z-score (rounded to 2 decimal places):

B. Probability (rounded to 4 decimal places):

5. There is a construction zone on a highway. The speeds of vehicles passing through this construction zone are normally distributed with a mean of 46 mph and a standard deviation of 4 mph.

Suppose that you want to make a speed limit such that only about 10% of the vehicles passing through this zone exceed the speed limit.

What should be the speed limit (rounded to the nearest integer)?