This data set, "Beer Goggles", provides median attractiveness ratings of 50 attractive or unattractive faces after consuming different amounts of alcohol. Variables: FaceType Attractiveness of the rated faces based on facial symmetry ('0' = unattractive, '1' = attractive). Alcohol Amount of alcohol consumed ('0' = Placebo group with 500 ml of non-alcoholic beer, '1' = Low-dose group with 500 ml of average strength beer (4% ABV), '2' = High-dose group with 500 ml of strong beer (7% ABV). Attractiveness Median of the 50 attractiveness ratings on a scale from 0 ("pass me a paper bag") to 10 ("pass me their phone number").

Assume that the attractiveness scores were distributed normally with a mean of 5 and standard deviation of 1.5.

Answer the following

What is the z score associated with a face that scored an 8?

What is the probability that a face chosen at random would be rated as less attractive than an 8?

What is the z score associated with a face that scored a 4?