Question

There are 80 players on the Rams Football Team. Assume that the list of players' heights is a normally distributed data set. The average of their heights is a normally distributed data set. The average of their heights is 73 inches (6'1") and the standard deviation is 3 inches.

a) Estimate the number of players who have height between 70 and 76 inches.

b) The Rams play the Chargers, whose players heights had an average of 42 inches and a standard deviation of 3 inches. The Chargers also have 80 players. How does the average of the list of heights of both teams together (all 160 players) compare to the average for only the Rams? What about the standard deviation? For each, are they larger, smaller, or the same?

Answer 1

Consider the random variable X as

X: Height of players of Rams Football team.

Given : X ~ N ( mu_x = 73, sigma_x = 3)

a)

From normal probability table

P(Z<1) =0.8413 and P(Z<-1) =0.1587

P(70 <X< 76) =0.6826

Number of players who have height between 70 and 76 inches = n₁ * P( 70 < X< 76) , n₁ = Total players = 80

= 80 * 0.6826

=54.608  

= 55 ( Approx)

Number of players who have height between 70 and 76 inches =55.

b) Y : Height of players of Chargers team

Given :

Average Height of all 160 players is

Since combined height is 52.5 which is less than average height of Rams football team.

Here n1= n2 = 80

The combined standard deviation of 160 players is

Value of combined standard deviation is 16.5605 which is larger than standard deviation of height of Rams football team.