The following table represents the age distribution of workers in Sunshine Enterprise.

a$.$ Calculate the mean age of the workers in Sunshine Enterprise.

b$.$ Calculate the standard deviation for the age.

Damansara Rally Auto Service Centre provides oil and lubricant services for cars. It is known

that the mean time taken for oil and lubricant services at this garage is $15$ minutes per car and

the standard deviation is $2\mathrm{.}4$ minutes. The management wants to promote the business by

guaranteeing a maximum waiting time for its customers. If a customer's car is not serviced

within that period, the customer will receive a $50\%$ discount on the charges. Assume that the

times taken for oil and lube service for all cars have a normal distribution. Answer the following

questions.

a$.$ If the company wanted to limit this discount to at most $5\%$ of the customers. What should

the maximum guaranteed waiting time be$?$

b$.$ What is the percentage that a randomly selected car serviced at this centre took more

than $20$ minutes?