The director of cost management for Odessa Company uses a statistical control chart to help management determine when to investigate variances. The critical value is $1$ standard deviation. The company incurred the following direct$-$labor efficiency variances during the first six months of the current year.

January $ $320$ F

February $870$ U

March $770$ U

April $970$ U

May $1,120$ U

June $1,600$ U

The standard direct$-$labor cost during each of these months was $$26,000.$ The controller has estimated that the firm$$s monthly direct$-$labor variances have a standard deviation of $$1,020.$

Required:

$2-$a$.$ Determine the cutoff value for investigation if the controller$$s rule of thumb is to investigate all variances equal to or greater than $6$ percent of standard cost.

$2-$b$.$ Based on the cutoff value, which month will have its direct$-$labor efficiency variance investigated?