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 61 87 74 72 73 19 56 81 79 83 75 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).
Accepted Solution
A:
Answer:a. The estimate of mean fan rating for the population of NFL games=68.08b. The estimate of standard deviation=18.8785Step-by-step explanation:Given The fan ratings for a random sample of 12 games follow:57, 61, 87,74,72,73,19,56,81,79,83 and 75a.Mean =[tex] \frac{ sum\;of\;data}{ total\;number \; of data}[/tex]Mean=[tex]\frac{57+61+87+74+72+73+19+56+81+79+83+75}{12}[/tex]Mean= 68.08b.[tex]\mid x-\bar x\mid[/tex] [tex]{\mid x-\bar x\mid}^2[/tex]11.08 122.76647.08 50.126418.92 357.96645.92 35.04643.92 15.36644.92 72.619249.08 2408.846412.08 145.926412.92 166.926410.92 119.246414.92 734.0646.92 47.8864Standard deviation=[tex]{\sqrt\frac{\sum{\mid x-\bar x\mid}^2}{n}[/tex]n=12[tex]\sum{\mid x-\bar x\mid}^2=4276.7872[/tex]Standard deviation=[tex]\sqrt\frac{4276.7872}{12}[/tex]Standard deviation=[tex]\sqrt{356.3989}[/tex]Standard deviation = 18.8785The estimate of the standard deviation for the population of NFL games=18.8785