Let X be a normal random variable with a mean of 3.9 and a standard deviation of 2.53. a) The zscore that corresponds to a particular data point (x) is 1.15. Calculate the data point. Give your answer to 2 decimal places. b) The area under the standard normal probability density function from 1.15 to innity is interpreted as the probability that X is: 0 less than or equal to x 0 equal to x O greater than or equal to x The coffee company imerican Expresso has a nev.I promotion where "Ifyou don't get your take away oo'ee within 180 seconds, It's free!". However, far too many coffees seem to have been given away since the promotion began. American Expresso has commissioned an independent study which found that \"die time to prepare a take away coffee at one of their stores is approximately normally distributed with a mean time of 207 seconds and a standard deviation of 21 seconds. You may nd this standard normal table useful throughout the following questions. a) Calculate the percentage of take away coffees that are given to customers for free according to the promotion. Give your answer as a percentage to 1 decimal place. Percentage of free coffees = \\:|% b) Shareholders are extremely unhappy with the tenTIs of the promotion and suggest that the time limit should be such that at most only 2.5% of take away coffees are given for free under the promotion. Calculate the time limit such that this requirement is satised. Give your answer as a whole number. Time limit = |:| seconds You consider yourself a bit of an expert at playing rockpaperscissors and estimate that the probability that you win any given game is 0.5. In a tournament that consists of playing 50 games of rockpaperscissors let X be the random variable that is the of number games won. Assume that the probability of winning a game is independent of the results of previous games. You should use the normal approximation to the binomial to calculate the following probabilities. Give your answers as decimals to 4 decimal places. in) Find the probability that you win at least 28 of the games. Pix 2 28) =E b) Find the probability that you win less than 21 games. mm c) Find the probability that you win between 20 and 30 games. Hzosxs301=\\:|