Question

7(B) The weight of an average footballer in team A is 220lbs. The standard deviation is 15lbs. A coach scouting a sample of 4 footballers will sign them if the sample mean weight is less than 215lbs.

1. What is the probability that he will sign them?
2. If the coach samples 100 players, what is the probability that the sample mean weight will be less than 215?

Answer 1

Solution :

Given that ,

mean =   = 220

standard deviation = = 15

(A)n = 4

= 220

=  / n = 15/ 4=7.5

P( < 215) = P[( - ) / < (215 -220) / 7.5]

= P(z < -0.67)

Using z table  

= 0.2514

probability=0.2514

(B)

n = 100

= 220

=  / n = 15/ 100=1.5

P( < 215) = P[( - ) / < (215 -220) / 1.5]

= P(z < -3.33)

Using z table  

= 0.0004

probability=0.0004