Question

A study of college football games shows that the number of holding penalties assessed has a mean 2.3 of penalties per game and a standard deviation 1.05 of penalties per game. What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.25 penalties per game or less? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Answer 1

Solution :

Given that,

mean = = 2.3

standard deviation = = 1.05

n = 40

= 2.3

₌ / n =1.05 40 = 0.1660

p ( 2.25)

P ( - /)   (2.25 - 2.3 /0.1660)

P( z    - 0.05 / 0.1660 )

P ( z -0.301 )   

Using z table

= 0.3817

Probability = 0.382