Let X be a random variable with a uniform distribution over the interval [-3,6]. Determine the mean of X. [The answer should be a number rounded to five decimal places, don't use symbols such as %]

where appropriate. 1. Experience has shown that the seeds from a certain variety of orchid have a 75% chance of germinating when planted under normal conditions. Suppose n seeds are planted, and let X be the random variable that counts the number of seeds that germinate. (a) What type of random variable is X? Indicate both the type and the appropriate parameters using the "~" notation. Write down the pmf of X, and do not forget to indicate the range of values that x can take on. X ~ px (x) = = (b) What is the minimum value of n so that the probability of at least five of the seeds germinating is at least 90%?

Mark has a batting average of 0.17. Let X be the number of hits in his next 16 at bats. What is the distribution of X? X      (,) Please show the following answers to 4 decimal places. What is the probability that he has exactly 7 hits? 0.0088 What is the probability that he has less than 7 hits?

The number of hours in a month a sample of 12 people chosen at random from a normal population work is as follows: 55,55,54,56,56,58,60,62,61,59,59,60. Can we conclude that the mean of the sample differs significantly from the assumed population average of 56 hours? Given that t11,0.05  2.201.