Let H be the discrete r.v. that represents the number of heads obtained when a fair coin is flipped for one time. What is the standard deviationof this distribution?

Today, the waves are crashing onto the beach every 5.6 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.6 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that wave will crash onto the beach exactly 0.7 seconds after the person arrives is P(x = 0.7) = d. The probability that the wave will crash the beach between 1.6 and 5.1 seconds after the person arrives is P(1.6 3.72) = f. Suppose that the person has already been standing at the shoreline for 0.8 seconds without a wave crashing in. Find the probability that it will take between 1.4 and 3.3 seconds for the wave to crash onto the shoreline. g. 65% of the time a person will wait at least how long before the wave crashes in? seconds. h. Find the minimum for the upper quartile. seconds.

On average, indoor cats live to 13 years old with a standard deviation of 2.3 years. Suppose that the distribution is normal. Let X = the age at death of a randomly selected indoor cat. Round answers to 4 decimal places where possible. a. What is the distribution of X? X NO b. Find the probability that an indoor cat dies when it is between 10.2 and 11.8 years old. c. The middle 40% of indoor cats' age of death lies between what two numbers? Low: years High: years

Let x denote the time taken to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race in 224 to 236 minutes? Round your answer to four decimal places. i