Question

Assume that the total number of goals scored per week in Spor Toto Super League has...

Assume that the total number of goals scored per week in Spor Toto Super League has

a Normal distribution with mean ? and standard deviation ?. The following data

summarizes the total number of goals scored in the first 12 weeks of the 2014-15 season.

Week # 1 2 3 4 5 6 7 8 9 10 11 12

Goals Scored 21 19 16 18 27 23 37 19 26 24 23 23

a) What is the average (?̅) and the standard deviation (?) of the total number of goals

scored per week in Super Toto Super League in the first 12 weeks?

b) What is the probability that the mean (?) of the total number of goals scored per week

in the Super Toto Super League is greater than 25? (Hint: You are asked to find

?{? ≥ 25}. Use ? =?̅−??⁄√? transformation where the random variable ? has a tdistribution with ? − 1 degrees of freedom.)

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Suppose, random variable X denotes total number of goals scored per week in Spor Toto Super League.

It is given that

But the values of mean as well as standard deviation are unknown. So we have to estimate those.

(a)

(b)

Population standard deviation is unknown. We use sample standard deviation for estimation of it. So the distribution to be used here is the t-distribution with the degrees of freedom 12-1 = 11.

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