Costa Coffee UK wants to introduce a new uniform for all its employees next year. They assumed that the only difference

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Costa Coffee Uk Wants To Introduce A New Uniform For All Its Employees Next Year They Assumed That The Only Difference 1 (57.8 KiB) Viewed 24 times

Costa Coffee UK wants to introduce a new uniform for all its employees next year. They assumed that the only difference between the uniforms is their height and that the employees' heights follow a normal distribution with mean 168cm and standard deviation 6cm (a) Calculate the probability that a randomly selected employee is i. less than 160cm tall (type 1 uniform) (3 marks) ii. between 160cm and 176cm tall (type 2 uniform) (3 marks) iii. more than 176cm tall (type 3 uniform) (2 marks) (b) The cost of type 1, type 2 and type 3 uniforms is £55, £65 and £75 respec- tively. Calculate the total investment required if Costa Coffee UK employs 20,000 people. (3 marks) (c) Before going ahead with the investment, Costa Coffee UK wants to check, at 5% level of significance, whether their workforce indeed has an average height of 168cm with standard deviation 6cm. They measured 100 employees and found that their average height was 170cm. i. State the null and alternative hypotheses. (2 marks) ii. What is (are) the critical value(s)? (2 marks) iii. Calculate the test statistic (3 marks) iv. What can you conclude? Why? (2 marks) v. Suggest one practical reason for your answer to part c (iv).