Fast bowling, also known as pace bowling, is an important component of the bowling attack in the sport of cricket. The objective is to bowl at a high speed and make the ball turn in the air and off the ground so that it becomes difficult for the batsman to hit it cleanly. Kalwant Singh is a budding Indian cricketer in a special bowling camp. While his coach is happy with Kalwant’s average bowling speed, he feels that Kalwant lacks consistency. He records his bowling speed on the next four overs, where each over consists of six balls.
It is fair to assume that Kalwant’s bowling speed is normally distributed with a mean and a standard deviation of 94 miles per hour and 2.8 miles per hour, respectively.
a. Construct the centerline and the upper and lower control limits for the chart. Plot the average speed of Kalwant’s four overs on the x̅ chart.
b. Is there any pattern in Kalwant’s bowling that justifies his coach’s concerns that he is not consistent in bowling? Explain.
