Let X be a normal random variable with a mean of 2.96 and a standard deviation of 2.58. a) The zscore that corresponds to a particular data point (x) is 0.55. Calculate the data point. Give your answer to 2 decimal places. b) The area under the standard normal probability density function from negative innity to 0.55 is interpreted as the probability that X is: 0 less than or equal to x 0 equal to x Q greater than or equal to x The coffee company American Expresso has a new promotion where "1'wa don't get your take away ooee within 180 seconds, It's freei". American Expresso has commissioned an independent study which found that the time to prepare a take away coffee at one of their stores is approximately normally distributed with a mean time of 156 seconds and a standard deviation of 24 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) Some shareholders are unhappy with the tem'ls 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. ve your answer as a whole number. Time limit = \\:| seconds Sam 'Vandelay' Johnson plays basketball for his college team. You've observed that the probability of Sam making a given shot is 0.55 and that the success of a given shot is independent of other shots. Over the course of many games, Sam takes 100 attempted shots at the basket. Let W be the random variable that is the number of successful shots. You should use the normal approximation to the binomial to calculate the probabilities in parts b) and c). Give your answers as decimals to 4 decimal places. a) Find the probability that Sam makes exacliy 5? successful shots from the 100 attempts. Hw=573=E b) Find the probability that Sam makes at most 57 successful shots from the 100 attempts. NEWS 1:) Find the probability that Sam makes between 50 and 60 successful shots from the 100 attempts. P{50$W$60)=\\:|