O Question 2 X P(x) 0.05 1 0.25 2 0.05 3 0.65 Find the mean of this probability distribution. Round your answer to one decimal place.Question 3 > X P(x) 0 0.3 1 0. 1 2 1 0.05 3 0.55 Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal placesQuestion 4 The television show Ghost Whistler has been successful for many years. That show recently had a share of 31, which means, that among the TV sets in use, 31% were tuned to Ghost Whistler. An advertiser wants to verify that 31% share value by conducting its own survey, and a pilot survey begins with 13 households have TV sets in use at the time of a Ghost Whistler broadcast. Find the probability that none of the households are tuned to Ghost Whistler. P(none) = Find the probability that at least one household is tuned to Ghost Whistler. P(at least one) = Find the probability that at most one household is tuned to Ghost Whistler. P(at most one) = If at most one household is tuned to Ghost Whistler, does it appear that the 31% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Ghost Whistler unusual?) Oyes, it is wrong O no, it is not wrong. Question 5 When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 37% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 45 of the dragon eggs to incubate. Consider all the possible samples of 45 dragon eggs. What is the mean number of yellow eggs in samples of 45 eggs? (that is the same as asking for the expected value of the number of yellow eggs) (Give answer correct to at least one decimal place.) mean = What is the standard deviation in the number of yellow eggs in samples of size 45? (Give answer correct to at least one decimal place.) standard deviation = What is the variance in the number of yellow eggs in samples of size 45? (Remember to calculate the answer using at least 5 decimal places, then give answer correct to at least one decimal place.) variance =Question 6 The Blacktop Speedway is a supplier of automotive parts. Included in stock are 10 speedometers that are correctly calibrated and two that are not. Three speedometers are randomly selected without replacement. Let the random variable @ represent the number that are not correctly calibrated. Complete the probability distribution table. (Report probabilities accurate to 4 decimal places.) P() 0 Find the mean of this probability distribution. (Appropriate rounding rules apply.) mean =Question 7 If a seed is planted, it has a 65% chance of growing into a healthy plant. If 6 seeds are planted, what is the probability that exactly 4 don't grow?Question 8 About 6% of the population has a particular genetic mutation. 800 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 800.. Question 9 Assume that a procedure yields a binomial distribution with a trial repeated n = 5 times. Use some form of technology to find the probability distribution given the probability p = 0.275 of success on a single trial. (Report answers accurate to 4 decimal places.) k P(X = k) 0 2 3 4 5