The heights of residents living in a college can be said to be normally distributed with mean 171.7 cm and standard deviation 10.1 cm. A student, Nick, is 172.6 cm tall. a) Compute the standardised value or z-score corresponding to Nick's height. Number (Enter your answer correct to at least 4 decimal places) b) Hence, compute the proportion of residents who are taller than Nick. Number (Enter your answer correct to at least 2 decimal places) It is known that Samim, another college student, is shorter than 62% of the residents in the college. c) How many standard deviations below or above the mean is Samim's height? Enter a negative value if below the mean and enter a positive value if the mean. Number (Enter your answer correct to at least 4 decimal places) d) Hence, compute Samim's height. Number cm (Enter your answer correct to at least 2 decimal places in centimeters)

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