The National Football League (NFL) polls fans to develop a rating for each football game. Each game is rated on a scale from 0 (forgettable) to 100 (memorable). The fan ratings for a random sample of 12 games follow. 57 62 87 74 73 72 19 58 81 78 83 73 a. Develop a point estimate of mean fan rating for the population of NFL games (to 2 decimals). b. Develop a point estimate of the standard deviation for the population of NFL games (to 4 decimals).

Answer:The point estimate of the standard deviation for the population of NFL games is [tex]\sigma = 18.1281[/tex]Step-by-step explanation:a) Develop a point estimate of mean fan rating for the population of NFL games The point estimate is the mean of the sample.The mean is the sum of the values divided by the number of values. There are 12 values, so:[tex]M = \frac{57+62+87+74+73+72+19+58+81+78+83+73}{12} = 60.08[/tex]The point estimate of mean fan rating for the population of NFL games is 60.08.b. Develop a point estimate of the standard deviation for the population of NFL games (to 4 decimals).This point estimate is the standard deviation of the sample.The standrd deviation of a N-cardinality set is given by the following formula:[tex]\sigma = \sqrt{\frac{1}{N-1}\sum_{k=1}^{N} (x_{k} - M)^{2}}[/tex]where [tex]x_{k}[/tex] is the element at the position k of the set and M is the mean of the set.For this sample, we have that the standard deviation(using a calculator) is:[tex]\sigma = 18.1281[/tex]The point estimate of the standard deviation for the population of NFL games is [tex]\sigma = 18.1281[/tex]