Question

In: Statistics and Probability

The average score for games played in the NFL is 22 and the standard deviation is...

The average score for games played in the NFL is 22 and the standard deviation is 9 points. 13 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.

  1. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
  2. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
  3. P(¯xx¯ > 19.1557) =
  4. Find the 72th percentile for the mean score for this sample size.
  5. P(20.0557 < ¯xx¯ < 25.0481) =
  6. Q1 for the ¯xx¯ distribution =
  7. P(∑x∑x < 284.1241) =
  8. For part c) and e), is the assumption of normal necessary? Yes or No

Solutions

Expert Solution

The average score for games played in the NFL is 22 and the standard deviation is 9 points. 13 games are randomly selected. Therefore, X ~ N (22,81)

a) X ~ N (22,81) then, the distribuion of is given by,

We know if, X~N(,) then,

As,

  

the distribuion of is  

i.e.

b)  the distribution of ∑x is given by,

We know, if X~N(,) then,

  

Hence,

the distribution of ∑x is

i.e.

c)

= 1 - 0.128 = 0.8720 (ans)

d) 72th percentile of mean scoe,

Z score of 72th percenticde is 0.583

  

= 0.720

Hence, 72th percentile is 22+0.583*2.50 = 23.4575 (ans)

e)

  

= 0.8890 - 0.2180 = 0.6710 (ans)

f) Q1 for distribution = 25th percentile of distribution.

  

Hence, 25th percentile is 22+ (-0.674)*2.50 = 20.3138 (ans)

g)

  

  

= 0.477(ans)

h) Yes,for part c) and e), the assumption of normal is necessary.

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