Does the new iPhone work correctly coming out of the box or…

Does the new iPhone work correctly coming out of the box or not.  Suppose whether the iPhone works correctly or not follows a binomial random variable and that out of all iPhones, 80% work correctly.  A random sample of n = 20 iPhones is analyzed.  Which of the following is closest to the probability that 15 or more but less than 18 work correctly.  

Reducing calories is a major trend for food manufacturers. …

Reducing calories is a major trend for food manufacturers.  General Mills advertises their best-selling Yoplait Greek Whips contains only 100 calories.  However, the actual number of calories varies.  Suppose the number of calories is distributed normally with a population mean of 96.2 calories and a population standard deviation of 2.1 calories.  A previous sample of 22 packages was taken and the sample mean was 99.4 calories with a sample standard deviation of 1.9 calories.  How large a sample should be taken in order to estimate the true mean number of calories to within a margin for error of 0.425 calories at the 95% confidence level?  

Pau’s partner asks her to tell them everything about her exe…

Pau’s partner asks her to tell them everything about her exes.  However, Pau does not want something she says to be held against her and therefore is not willing to disclose. Her partner feels hurt that she won’t confide.  This can be described as an imbalance in which relational dialectic?

Crystal wants some time alone because she feels a need to ge…

Crystal wants some time alone because she feels a need to get in touch with herself as an individual. However, her romantic partner wants her to spend as much time together as possible. The tension in this example illustrates the ____ ____ relational dialectic.