3 A sample of 12 games of bowling for an amateur bowler resu

3) A sample of 12 games of bowling for an amateur bowler resulted in the following scores:

233 170 205 208 163 178 219 140 155 211 224 215

Assume the scores for this bowler are normally distributed.

a) Find the sample mean. Use an Excel function.

b) Find the sample standard deviation. Use an Excel function.

c) Construct a 94% confidence interval for the mean bowling score for this bowler.

a) Excel Function for calculating sample mean is: [=Average(A1:A12)]

Mean of this sample shall be : 193.4167

b) Excel Function for calculating sample standard deviation is: [=STDEVA(A1:A12)]

Standard Deviation of this sample shall be: 30.62815

c) Confidence coefficient is the critical value of z for 96% confidence level = 2.054

Upper Bound of the Confidence Interval = Mean + 2.054( standard deviation)

Upper Bound of the Confidence Interval = 193.42 + 2.054(30.63) = 193.42+62.91 = 256.33

Lower Bound of the Confidence Interval = Mean - 2.054( standard deviation)

Lower Bound of the Confidence Interval = 193.42 - 2.054(30.63) = 193.42-62.91 = 130.51

Hence, the confidence interval at 94% is 130.51 to 256.33