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In the year 2031, Giselle Lara is a leading UX (user experience) designer. Giselle is presently researching the time to navigate through a set of tasks on a new user interface. Suppose this time is normally distributed with a mean of 15 minutes and a standard deviation of 2.6 minutes.

a) In a random sample of 9 people, what is the probability the sample mean is more than 18.1 minutes? Would you classify this observation as an outlier? Why or why not?

b) What is the probability a randomly selected person took longer than 18.1 minutes? Would you classify this observation as an outlier? Why or why not?

c) What is the Interquartile Range (IQR) for the times?

d) If you took a random sample from this population and constructed a box-and-whisker plot, approximately what would be the three values on the box?

e) One person's time was 1.75 standard deviations above the mean. What was this person's time?

f) Using Z > 2 as a criterion for an outlier, what is the minimum sample size such that a sample mean of 16 minutes would be classified as an outlier?

g) Giselle is developing new user interface with the goal of decreasing the time for users to navigate through the interface. Giselle desires the population mean to be such that in a random sample of 15 people the probability the sample mean is less than 4 minutes is 0.7 (assume the population standard deviation = 2.6 minutes). In order to accomplish Giselle's goals, the population mean (to the nearest tenth) is ___?