Question

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

Answer 1

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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