2016-04-09 15:16:06
The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. if you select a random sample of 9 tennis balls, what is the probability that the sample mean is between 2.62 and 2.64 inches
2016-04-09 16:21:28

For us to calculate for the probability of picking 2.62 and 2.64 in 9 balls we proceed as follows; The z score is given by: z=(x-mean)/s.d z score of 2.62 will be: z=(2.62-2.63)/0.03 =-0.3333 the probability associated with the above z-score is: P(2.62)=0.3707 The z-score of 2.64 will be: z=(2.64-2.63)/0.03 z=0.3333 The probability associated with this z-score will be: P(0.3333)=0.6293 therefore the probability of obtaining a sample mean between 2.62 and 2.64 will be: 0.6293-0.3333 =0.296 thus the answer is 0.296