Greggs, a chain of popular bakery stores, wants to introduce a new uniform for all its employees next year. They assumed

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Greggs, a chain of popular bakery stores, wants to introduce a
new uniform for all its employees next year. They assumed that the
only di􏰀erence between the uniforms is their height and that the
employees' heights follow a normal distribution with mean 170cm and
standard deviation 8cm.
(a) Calculate the probability that a randomly selected employee
is
i. less than 160cm tall (type 1 uniform)
ii. between 160cm and 180cm tall (type 2 uniform)
iii. more than 180cm tall (type 3 uniform)

(b) The cost of type 1, type 2 and type 3 uniforms is 55 Pounds, 65
Pounds and 75 pounds respectively. Calculate the total investment
required if Greggs employs 18,750 people.
(c) Before going ahead with the investment, Greggs wants to check,
at 5% level of significance, whether their workforce indeed has an
average height of 170cm with standard deviation 8cm. They measured
100 employees and found that their average height was 167cm.
i. State the null and alternative hypotheses.
ii. What is(are) the critical value(s)?
iii. Calculate the test statistic
iv. What can you conclude? Why?
v. Suggest one practical reason for your answer to part c
(iv).