The cost of catering services for a sample of 25 gatherings is normally distributed with mean $6000 and standard deviation 750.

(i)What probability of gatherings cost more than $6200?

(ii)What probability of gatherings cost between $5500 and $6000?

(iii)Determine the maximum cost required for a gathering to be in the bottom/cheapest

10% of catering service cost.

(iv)Construct a 90% confidence interval for the mean cost of catering service. Give an

interpretation of this interval.