Question

The average score for games played in the NFL is 21 and the standard deviation is 9.3 points. 10 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¯ < 20.9887) =
4. Find the 70th percentile for the mean score for this sample size.
5. P(20.5887 < ¯xx¯ < 23.3705) =
6. Q1 for the ¯xx¯ distribution =
7. P(∑x∑x < 183.887) =
8. For part c) and e), is the assumption of normal necessary? YesNo

Only needing help with # C, E, F.

Unless you want to do all problems, is up to you. Thank you!

Answer 1

Consider

X: Scores for the games playes in NFL.

E(X) = 21 and SD(X) = 9.3

n = number of games played

a) : Avregae sample score.

Assume the distribution of X is normal. Each game is independent to each other.

The samping distribution is normal with mean = 21 and variance

b) = Total score played in 10 games.

The distribution of total score is normal with mean and variance

c)

= P(Z< -0.0038) since

From normal probability table

P(Z< -0.0038) =0.4985

d) Let a be 70th percentile of mean score.

---------------(I)

From normal probability table

P( Z< 0.5244) = 0.70 --------------------(II)

From (I) and (II)

70th percentile of mean score is 22.5422.

e) = P ( -0.1399 < Z < 0.8061)

=P( Z< 0.8061) - P(Z < -0.1399)

From normal probability table

P( Z< 0.8061) =0.7899 and P( Z< -0.1399) =0.4444

Hence

f)

---------------(III)

from normal probability table

P( Z< -0.6745) = 0.25 --------------(IV)

From (III) and (IV)

Q1 for the distribution is 19.0164.