When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 18% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 46 of the dragon eggs to incubate. Consider all the possible samples of 46 dragon eggs. What is the mean number of yellow eggs in samples of 46 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 46?
(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 46?
(Remember to calculate the answer using at least 5 decimal places, then give answer correct to at least one decimal place.)
variance =

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?