Probstat/week8 practice 2

This is part of probstat.

To compute the cdf of standard normal random variable, you can use a table from wikipedia.

Basic practice

Let Z be a standard normal random variable (whose mean is 0 and variance is 1).

1. Find P{ Z >= 0 }.

2. Find P{ Z >= 0.5 }.

3. Find P{ Z >= 1 }.

4. Find P{ Z >= -0.3 }.

5. Find P{ -1 <= Z <= 0.1 }.

6. Find P{ Z <= 0.2 }

7. Approximate the minimum value a such that P{ Z >= a } <= 0.1.

8. Approximate the minimum value a such that P{ -a <= Z <= a } >= 0.7.

9. The download speed of a file to your computer is normally distributed with parameters $\mu =5$ Mbps and $\sigma ^{2}=0.5$. What is the probability that you get the download speed faster than 6 Mbps? What is the probability that your speed is below 4 Mbps?

10. The average height that Somchai the athlete can jump is 2 m with variance 0.16. Today to win, Somchai has to jump higher than 2.4 m. What is the approximate probability that Somchai will win?